Research Article  Open Access
SuperTwisting Sliding Mode Control for Gearless PMSGBased Wind Turbine
Abstract
In recent years, the complexities of wind turbine control are raised while implementing grid codes in voltage sag conditions. In fact, wind turbines should stay connected to the grid and inject reactive power according to the new grid codes. Accordingly, this paper presents a new control algorithm based on supertwisting sliding mode for a gearless wind turbine by a permanent magnet synchronous generator (PMSG). The PMSG is connected to the grid via the backtoback converter. In the proposed method, the machine side converter regulates the DClink voltage. This strategy improves lowvoltage ride through (LVRT) capability. In addition, the grid side inverter provides the maximum power point tracking (MPPT) control. It should be noted that the supertwisting sliding mode (STSM) control is implemented to effectively deal with nonlinear relationship between DClink voltage and the input control signal. The main features of the designed controller are being chatteringfree and its robustness against external disturbances such as grid fault conditions. Simulations are performed on the MATLAB/Simulink platform. This controller is compared with ProportionalIntegral (PI) and the firstorder sliding mode (FOSM) controllers to illustrate the DClink voltage regulation capability in the normal and grid fault conditions. Then, to show the MPPT implementation of the proposed controller, wind speed is changed with time. The simulation results show designed STSM controller better performance and robustness under different conditions.
1. Introduction
Recently, wind energy is a rapidly growing source of electricity [1, 2]. Installed wind power generation is expected to exceed 760 GW by 2020 in the world [3]. Therefore, the significant amount of power generation capacity belongs to wind power. In the past, wind farms could be disconnect from the grid in the grid side fault conditions, but nowadays, the modern grid codes, in addition to not allowing the separation of the grid to wind turbines, require them to perform some auxiliary tasks in grid fault conditions. For instance, Danish grid code forces wind farm to follow lowvoltage ride through (LVRT) requirements in fault condition according to Figure 1 [4].
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Among different types of wind turbines, doubly fed induction generators (DFIGs) and permanent magnet synchronous generators (PMSGs) are of attractive types in wind farms [5]. Due to advantages, developments in semiconductor switching devices and highreliability and efficiency, the use of PMSG is growing.
In traditional control of backtoback converter, machine side converter (MSC) performs the maximum power point tracking (MPPT) and the grid side converter (GSC) regulates the DClink voltage [6, 7]. Hence, when grid faults occurred, the DClink voltage may be increased because MSC does not sense grid fault and GSC loses its own control on DClink voltage regulation [8]. To overcome this problem, the GSC and MSC tasks can be changed [9, 10]. Due to the nonlinear relationship between DClink voltage and input control signal, different nonlinear controls are presented [11, 12].
Among the modern nonlinear control, sliding mode control has good feature because it is robust with respect to system parameter uncertainties and external disturbances [13]. The main drawback of conventional sliding mode control is chattering. To reduce chattering, several methods are introduced. One of the attractive chatteringfree sliding modes is high order sliding mode (HOSM) [14, 15]. But the main problem in the implementation of HOSM algorithms is the increasing information demand. The supertwisting sliding mode (STMC) is one of HOSM that does not need additional information [16, 17].
Several papers use the HOSM to enhance LVRT capability in PMSGbased wind turbines [18–20]. Nevertheless, all of these works use traditional control of backtoback converters. In fact, they cannot keep the DClink voltage in safe range in deep voltage drops. Therefore, they need to use external devices which result in the overall cost increases. As mentioned before, by exchanging the task of converters, the DClink voltage is kept in safe range, MSC regulates DClink voltage, and GSC controls MPPT. In present paper, the supertwisting sliding mode control method is employed in the new control structure.
It can be mentioned that the new contribution of the proposed method is implementing a HOSM controller for the gearless high inertia PMSGbased wind turbine, in which no additional instrument is required to implement LVRT without imposing stress to the DClink capacitor. In fact, the grid voltage drop and the wind variations are considered as an external disturbance. Furthermore, the chattering is eliminated and the controller does not need additional information.
In this paper, wind energy conversion system model, including modeling of the wind turbine, PMSG, DClink, and the grid is presented in Section 2. In Section 3, first, the brief review of STSMC is presented; then full STSM controllers for backtoback converters are designed. Section 4 proves the improvement of the new control strategy by comparing with the conventional approach on the MATLAB/Simulink. Finally, in Section 5, conclusions are presented.
2. Description of Wind Energy Conversion System
The schematic of the PMSG wind power system is shown in Figure 2. The modeling of each section has been introduced in the following subsections.
2.1. Modeling of Wind Turbine
The mechanical output power of wind turbine is given by the following equation:The turbine power coefficient is defined by the following equations [21]:The tipspeed ratio (λ) depends on the shaft speed () and the wind speed as given below:From (1) and (4), the turbine torque is given asThe equation of motion of singlemass modeling of the mechanical system is expressed aswhere is the electromagnetic torque of the generator.
2.2. Modeling of PMSG
A dynamic mathematical model of a surfacemounted PMSG is presented in the synchronous dq equivalent circuits as [22]
The electromagnetic torque from the generator is given as
2.3. Modeling of DCLink
The DClink is the interface between the generator and the grid. The dynamic DClink voltage equation can be expressed bywhere and are the generator and the backtoback converters losses and the grid power, respectively. In this study, it is supposed that converters are lossless.
2.4. Modeling of Grid
The GSC is connected to the point of common coupling (PCC) by RL grid filter and a coupling transformer. In this study, it is modeled by RL that the state equations in the dq reference frame can be expressed aswhere ω_{f} is the angular frequency.
The equations of instantaneous injected active and reactive powers to the PCC are expressed as
If the PCC voltage space vector is oriented on daxis, , then
Now, let us introduce the state variables , , , , , .
The statespace equations obtained up to now are put together to obtain a statespace model of the whole system. It is supposed that the MSC and GSC are ideal and they produce the desired voltages. In fact, the average model is used for GSC and MSC. For convenience, the statespace models of the whole system are rewritten as
3. Control of BacktoBack Converters
In this section, new controllers for the backtoback converters are designed using secondorder sliding mode. Among several proposed modern techniques, the sliding mode provides more advantages such as robustness and highaccuracy solution especially for nonlinear systems under uncertainty conditions and external disturbances [23]. The main disadvantage of the classic sliding mode is the chattering problem. Though, the secondorder sliding mode is appropriate to obtain chatteringfree control and guarantees a finitetime reaching phase [24]. In Section 3.1, secondorder sliding modes are briefly introduced, then, in Section 3.2, supertwisting controller that is one of attractive secondorder sliding mode controllers will be presented.
3.1. A Brief Introduction of SecondOrder Sliding Modes
As mentioned before, the main disadvantage of firstorder sliding mode control (FOSMC) is a chattering problem. This effect consists of the oscillation of the system variables around the sliding surface, which causes a discontinuous control signal. This effect can disturb or damage the physical system. One of the interesting ways to eliminate or reduce chattering effect is using HOSM. In this technique, the higher order time derivatives of sliding surface keep to zero [24]. As a result, this action mitigates the chattering effect. But, the increasing information demand is the main problem in the implementation of HOSM algorithms. Generally, rth order sliding controller requires the knowledge of (r1)th order of time derivative. Thus, a rth order sliding mode is determined by
Hence, the secondorder sliding mode controller is simple. In fact, it needs the knowledge of the firstorder time derivative of the sliding surface. These controllers require realtime measurement of or at least of .
Among several secondorder sliding mode controllers, the supertwisting controller has a good feature because it does not need the knowledge of . The supertwisting controller can be used instead of the firstorder (conventional) sliding mode using the same available information.
3.2. SuperTwisting Controller
Consider the nonlinear dynamic system given by [24]where , , and the smooth functions , , are unknown. From (24), the time derivative of the sliding surface can be expressed aswhere and are smooth functions that for some positive constants , , , , and the following relations can be held.and the input control signal can be defined aswhere and should be satisfied with the following conditions:
Figure 3 shows the phase portrait in the supertwisting controller.
3.3. Generator Side Converter Controller
As mentioned in the Introduction, to suppress DClink overvoltage in a grid fault condition and implement LVRT, DClink voltage is controlled by MSC. In this method, GSC implements MPPT.
The reference value of daxis current of the generator is zero to reduce the copper loss and to avoid demagnetization of permanent magnets. The qaxis voltage of generator (qaxis input control signal) is produced by DClink voltage surface.
3.3.1. DAxis Controller Design
The goal of the daxis controller is keeping the daxis current of the generator to zero. Hence, the control object can be expressed by the sliding variable:where is a positive constant. By taking the first derivative of and using (18), we have
Suppose that the control signal, , can be divided into known and unknown terms. Equation (30) can be rewritten aswhere is known term of the controller and is the unknown term of the controller. By selecting as the following form: and substituting (32) into (31), we have where
According to (33), we can use supertwisting sliding mode control. Hence, the unknown term of the daxis controller can be expressed bywhere the values of control parameters are given in the Appendix.
3.3.2. QAxis Controller Design
The qaxis controller is regulating DClink voltage in suitable constant value in all conditions such as wind variation condition and grid fault condition that the DClink voltage may be varied. Also, the relationship between DClink voltage and the qaxis controller signal is nonlinear. Hence, the control object can be expressed by the sliding surface:
Let us introduce sliding variable aswhere is derivative of . and are positive constants. By dividing known and unknown terms and taking the derivative of and substituting (19) and (20) in it, we have: where
According to (39), we can use supertwisting sliding mode control. Hence, the unknown term of qaxis controller can be expressed by
As a result, qaxis control law becomes
3.4. Grid Side Converter Controller
The GSC has two main tasks: first, MPPT control of wind turbine, second, reactive power supporting the grid in different situations such as grid voltage drop. The daxis controller performs MPPT control and qaxis controller supports reactive power.
3.4.1. DAxis Controller Design
As mentioned above, MPPT is implemented by the daxis controller of GSC. There are several approaches to implement MPPT that among them optimal power control (OPC) can be applied to PMSGbased wind turbines [25]. In this design, the OPC method is used.
Considering (4) and (5) and replacing the optimal value of and the wind turbine mechanical torque can be given as a function of , as follows:where .
The optimal mechanical power of the turbine can be obtained by multiplying both sides of (43) by . Thus
The PCC power reference can be obtained by subtracting the losses of optimal mechanical wind turbine power aswhere is the RL filter loss. From (15) and (45), the daxis reference current is obtained as
It should be noted that, in voltage drop conditions, Danish grid code enforces wind power plants to inject reactive current to PCC according to Figure 1. Hence, the daxis current should be limited to produce reactive current by the qaxis controller because the current capacity of power electronic converter is limited. The value and upper limit of dq axis currents in different conditions becomeswhere , , and are the per unit of rated current of the converter, the per unit of the upper limit of daxis current, and the per unit of the upper limit of qaxis current, respectively. , , and are the per unit of daxis voltage in PCC, the per unit of daxis current, and the per unit of qaxis current, respectively. Now, by calculating the daxis current from (46) and applying (47), the daxis controller can be designed.
The control objective can be expressed by the sliding variable:where is a positive constant. By taking the first derivative of and using (21), we have
Suppose that can be divided into known and unknown terms. Equation (49) can be rewritten aswhere is known term of the controller and is an unknown term of the controller. By selecting as the following form and substituting (51) into (50), we havewhere ,
According to (52), we can use supertwisting sliding mode control. Hence, the unknown terms of the daxis controller can be expressed by
As a result, the qaxis control law becomes
3.4.2. QAxis Controller Design
The main task of the qaxis controller is reactive power supporting the grid in different conditions. The qaxis current reference can be produced by reactive power demand of PCC by (16) in normal condition and by (47) in the grid voltage drop conditions. The design procedure is similar to the daxis controller design. Hence, to avoid repeating, it is written only sliding variable and qaxis control low equation.
As a result, qaxis control law becomes
4. Simulation Results
To evaluate the performances of designed supertwisting sliding mode control in the PMSGbased wind turbines, the several simulations have been carried out on the MATLAB/Simulink software. Then this method is compared with the PI controller [8] and FOSMC [13]. The parameters of a 1.5 MW PMSGbased wind turbine and grid characteristics are given in Table 1.

4.1. Operation with Symmetrical Grid Faults
As mentioned above, the relationship between the DClink voltage and the generator qaxis input control signal is nonlinear. In controlling and regulating the DClink voltage at a constant value in all conditions such as grid fault situation, three controllers (PI, FOSMC, and STSMC) are compared. To evaluate the performances of these controllers, symmetrical voltage drop similar to the Danish grid code (Figure 1) at t=5s is applied as shown in Figure 4.
Figure 5 shows the DClink voltage variation with three controllers. As shown in Figure 5, the STSMC has the best performances in DClink voltage control in both starting time and grid voltage drop. According to Figure 5(a), the FOSMC has higher chattering in all time. In addition, STSMC has the fast starting time (Figure 5(b)). Furthermore, in the PI controller, the peak of the DClink voltage reaches 1556 V while in STSMC, it is less than 1510 V (Figure 5(c)).
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Figure 6 shows the qaxis current of the generator. This component of current controls the DClink voltage. As shown in Figures 6(a) and 6(b), the STSMC has fast response in the grid voltage drop. Hence, this subject can reduce the DClink overvoltage. The FOSMC has chattering and it can fatigue the DClink capacitor.
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The daxis current of the GSC is shown in Figure 7. According to Figure 7, PI controller has worst performance in the grid fault condition.
In Figure 8, qaxis current of the GSC is shown. Although all of the controllers satisfy the injecting reactive current according to the grid code, similar to Figure 7, the PI controller does not have good performance.
As mentioned above, one of the main drawbacks of FOSMC is chattering especially in the input of controllers that results in chattering in systems variables. Figure 9 shows the input control signals to the MSC and GSC in the FOSMC. As shown in Figure 9, the amplitude of chattering in controller signals is extremely high. To overcome this drawback, the STSMC is suitable solution. Figure 10 shows input control signals to the MSC and GSC in the supertwisting controller. As it is seen, the chattering in the input control signals is reduced.
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The phase portraits corresponding to the reaching phase of the dq axis sliding variables of the generator side and grid side controllers in the STSMC are depicted in Figure 11. These plots (Figures 11(a)–11(e)) show the features illustrated by supertwisting controllers during the system convergence toward .
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To show the compliance of the grid code requirements in reactive current injection by the designed system, the injected reactive current versus grid voltage drop is shown in Figure 12. As shown in Figure 9, the designed controller injects reactive current similar to Figure 1(b).
4.2. Operation with Asymmetrical Grid Fault
To evaluate the performance of proposed controller in asymmetrical voltage drop, a singlephase voltage drop is simulated in phase A. Figure 13 shows the PCC voltage in singlephase voltage drop.
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Figure 14 shows DClink voltage variation in singlephase voltage drop. As shown, there is low amplitude fluctuation in the DClink voltage in asymmetrical voltage drop. However, the STSMC has good performance in this condition.
4.3. Operation in Normal Condition
To emulate the performance of the supertwisting controllers in normal condition, a wind velocity profile is defined as expressed in [22]:
The amplitude and frequency of wind velocity components are given in Table 2. The resultant wind velocity profile is as shown in Figure 15(a). Figure 15(b) shows wind turbine power (P_{m}) and injected active power (P_{grid}) to PCC. Figure 15(c) shows the power coefficient of the wind turbine. The average of C_{p}is 0.4493 from t=5s to t=40s. Of course, when the wind speed increases from 12 m/s the turbine power reaches the nominal value. Hence, the pitch angle controller will be active to set turbine power in nominal power as shown in Figure 15(d). As a result, C_{p} is slightly less than 0.48. It is clear that with the STSMC, also, MPPT is perfectly achieved. As shown in Figure 15(e), the DClink voltage is fixed in 1500 V. This shows the robust DClink voltage against wind fluctuations.

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5. Conclusions
This paper presents a supertwisting sliding mode control for gearless PMSGbased variable speed wind turbines. First, the mathematical models of the wind turbine, PMSG, DClink, and grid are represented. Then the supertwisting controllers are designed for generator and grid side converters. The proposed controller is compared with the proportionalintegral (PI) controller and firstorder sliding mode controller (FOSMC). By applying the proposed controller, the DClink overvoltage is significantly reduced rather than the PI controller. Furthermore, chattering is reduced in input controller signals and DClink voltage. Also, the reactive current injection is done according to modern grid codes. In order to evaluate the performance of the supertwisting controllers in unbalanced voltage drop, it has simulated a singlephase voltage drop. Furthermore, designed controller can greatly do the MPPT and regulates the DClink voltage in reference value in normal condition. The robustness and effectiveness of the designed supertwisting controllers in different conditions are confirmed by simulation results.
Appendix
Nomenclature
Symbols:  Air density () 
:  Radius of blade (m) 
:  Pitch angle (°) 
:  Tipspeed ratio 
:  Power coefficient 
:  Wind speed () 
:  Total equivalent inertia () 
:  Viscous friction coefficient ) 
:  Number of poles 
:  Shaft speed () 
:  Electrical angular velocity () 
:  Resistance () 
:  Inductance () 
:  DClink capacitance () 
k:  Positive gain 
:  Grid side inverter voltage 
:  Voltage () 
:  Current () 
:  Flux () 
d, q:  Direct and quadrature components 
s:  Stator of machine 
f:  Grid side 
dc:  DClink 
ref:  Reference. 
Data Availability
The MATLAB files data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflict of interest.
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Copyright
Copyright © 2019 Mojtaba Nasiri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.