Hybrid nonlinear control strategies for performance enhancement of a doubly-fed induction aero-generator: design and DSP implementation

Received Aug 30, 2020 Revised Jun 18, 2021 Accepted Jul 8, 2021 This paper reports on the design and implementation in DSP as hardware in the loop of a nonlinear control strategy for a grid-connected variable speed wind turbine using a doubly fed induction generator (DFIG). The objective of this work is to build a real-time nonlinear hybrid approach combining Backstepping control and sliding mode control strategies for DFIG used in wind energy conversion systems (WECS). The results of the DSP implementation are discussed and qualitative and quantitative performance evaluations are performed under various disturbed conditions. The implementation is performed using the TMS320F28335 DSP combined with the MATLAB/Simulink (2016a) environment. The experimental results have been satisfactorily achieved, which implies that the proposed strategy is an efficient and robust approach to monitor the WECS.

friendly. For these reasons, wind power generation has attracted a great deal of interest in recent years [1], [2]. Several types of electrical machines have been used for energy conversion. However, it would seem that the asynchronous machine is the obvious option in applications using wind turbines. Fixed speed asynchronous machines have to operate around the synchronous speed, because the frequency is imposed by the grid, and the rotor speed is practically constant. The interest of variable speed for a wind energy system is to be able to operate over a wide range of wind speed and to be allowed to get the maximum power from it through the MPPT (maximum power point tracking) strategy, for each speed, for this type of application DFIG associated with power electronics converters is today the most employed machine [3].
These electrical machines have external disturbances, nonlinearities and parametric errors. Conventional linear methods are becoming ineffective, unable to accommodate such phenomena and often give less satisfactory results [4]- [6]. To overcome this problem, the trend in current research has been towards robust nonlinear system controls that give acceptable performances over wide operating ranges. There are many methods developed in the literature use the Robust control to command these systems. The following can be cited as examples the H-infinite control methods [7], [8], the predictive control [9], the fuzzy logic control methods [10]- [16], non-linear control by static or dynamic state feedback [11]- [13], the variable structure control methods [14], [15]. However, the majority of these methods require a lot of calculations and are not really adapted to the WECS-based DFIG control. Only the variable structure control, more commonly called sliding mode control, and the backstepping control seem to be suitable for this topic [14]- [25].
In recently published studies [14]- [25], it has been shown that backstepping control and sliding mode control have given interesting results in terms of robustness and the quality of the produced power. In the present work, the authors intend to improve the performance of DFIG in wind power generation by designing a real-time non-linear hybrid approach combining backstepping control (BC) and sliding mode control (SMC) strategies mainly for robustness to WECS parameter variations, taking into account the nonlinearity of the system model. Hardware-in-the-loop (HIL) simulation is a technology that has been emerging in recent years. It consists of validating the developed control laws without the need to use the physical system, it is enough to have a simulated model of the system in question. HIL simulation is therefore widely used in the design of controllers. HIL testing is proving to be an important and universally accepted tool for the control and design of system equipment and power electronics [14]- [27].
The paper is structured in the following way: the Section 2 is devoted to the Methods and Materials. This section is divided to 3 parts. In part 1, the WECS configuration will be presented by establishing the models of the different elements constituting the WECS. The control strategies are carefully elaborated in part 2. The DSP implementation in the loop is presented in part 3. Section 3 is devoted to the results of the validation of the implemented controls.

Modelling of the wind turbine conversion chain based on a DFIG
A description of the different components of the DFIG-based WECS is shown in Figure 1. The structure of the system can be divided into two main parts. The mechanical part which consists of the turbine, the gearbox and the drive shaft. Then, the electrical part which is composed of the DFIG whose stator is connected directly to the electrical grid, as long as the rotor is connected to the grid by two static bidirectional power converters and a DC bus in a configuration called Back to Back.

Wind turbine
The aerodynamic torque, which is converted by a wind turbine, depends on the power coefficient Cp. It is given by: The ratio λ is expressed by the (2) relation: By applying the fundamental of dynamics, we get the evolution of mechanical speed (the rigidity is very low it can be neglected) [14]- [20]:

DFIG model
The electrical equations of the DFIG in the Park frame are written as [17]- [21]: To be able to easily control the wind turbine's output, the coordinate system (d-q) is oriented to align the daxis with the stator flux ϕs:

A hybrid backstepping-sliding mode control of the DFIG powers used in WECS
In this part, we focus on the application of the backstepping method associated with the sliding mode control of the double-feed induction generator. We'' ll establish the command value expressions based on the established model in the previous section.

Rotor-side converter (RSC)
The backstepping's command law expressions are as [25]: The expression of the backstepping stabilizing command associated with the sliding mode setting is derived as: Where 5 k , 51 k , 6 k , and 61 k are positives constants. To ensure the convergence of Lyapunov's candidate function, we must have verified that:

Grid-side converter (GSC)
The backstepping's command law expressions are as [25]: In order to ensure a faster dynamic of the grid current components, 7 k , 71 k , 8 k , and 81 k are chosen to be positives parameters. Therefore:

Tracking of the maximum power point of the proposed wind system
In order to extract the maximum power, the specific speed must be set to its optimal value in order to obtain the maximum power coefficient . The power coefficient p c must be maintained at its maximum value in order to reach the , which is given by (15): the tacking error is given by: by combining (15), (16) and (4), the dynamics of this error is obtained: in order to stabilize the system, a Lyapunov function is defined, such as [23]: where P is a positive matrix chosen as follows: the dynamics of Lyapunov's function is: with a judicious choice of the relationship between the error and its derivative, such as: where m is a positive constant. The (20) becomes: by combining (17) and (22), the expression of the reference torque can be deduced.
Using the same logic as (23), the expression of the backstepping stabilizing command associated with the sliding mode setting is derived as: where m and n are positives constants.

Implementation of the controller's algorithms on DSP
The integration of the DSP card with MATLAB/Simulink software provides a high-performance, high-quality development environment. Co-simulation using the DSP board allows testing a new electronic control unit (ECU) in a virtual environment without real devices or physical machines. After modelling the entire system in Simulink software, the block diagrams of the simulated model can be transferred to DSP via code created by SimulinkCoder. The real-time simulated model is compiled, downloaded, and started automatically. The C2000 library of Texas Instruments DSP family on simulink embedded coder was used to generate the code to be implemented on TMS320L28335 DSP (Figure 2). The main strength of TMS320L28335 DSP lies in the many peripherals it has that has made this DSP a very powerful universal control machine [27]. It has very high performance, so even complex control algorithms can be effectively implemented on this platform. Figure 3 presents the model to be implemented on the DSP and hardware in the loop of the suggested controls. Figure 4 depicts the WECS model under MATLAB/Simulink communicating with the DSP and Figure 5 displays the controls hardware in the loop interacting with MATLAB/Simulink.  The reference rotor speed and the real measure speed from the proposed controls are shown in Figure 6. The results demonstrate quick convergence and good tracking performance of the real mechanical speed during the whole wind speed profile. The error between the speed reference and the real speed is very small.
The optimal power extracted from the wind turbine by the MPPT algorithm is used as the reference power. Thus, in order to guarantee a unit power factor, it is necessary to have a zero reference for the reactive  Figure 7 and Figure 8 show respectively the response of the two powers (active, reactive) of the DFIG, and it can be noted that both powers follow these references successfully, and with a fast response time. Figure 9 and Figure 10 show the waveforms of the currents. The stator and rotor currents both have a sinusoidal waveform. Moreover, the frequency and amplitude of the rotor current vary as a function of the generator speed.
As can be seen in Figure 11, the DC link voltage evolution is extremely satisfactory. The results of the variation of the machine parameters are shown in Figure 12. The DFIG parameter variations show a very small increase in the time response of the proposed control strategy. Furthermore, this result shows a clear effect in steady-state error when using a hybrid control compared to those obtained with a backstepping control strategy [25]. It can be concluded that the proposed control is more robust than the BC. On the other hand, the disadvantage of the sliding mode [14] called chattering phenomenon is overcome by using the hybrid backstepping-sliding mode control. In accordance with the result: i) the results of the implementation of the DSP as a HIL present the performances in terms of set point monitoring, static errors and robustness, and ii) the results of the implementation of the control proposed on DSP as hardware in the loop converge to those obtained with conventional simulations on Simulink.
To validate the performances of the proposed control, a literature review in recent works based on PI regulation of wind energy systems using DFIG [6]- [17] has been done. As a result, for the PI controllers, the effect of the coupling between the two powers is observed because a step imposed on one of the two powers (active or reactive) induces an important dismissal of the powers compared to the reference value and a time to return to the initial state. Thus, during parametric variations, there is an increase in the amplitude of the rejection and in the return time. Therefore, the proposed hybrid strategy shows its superiority by effectively rejecting the effects of disturbances, hence the powers follow their references perfectly. As well as the variations of the parameters of the system have no effect on the evolution of the power. nonlinear hybrid approach provides good static and dynamic performances of the system; Setpoint follow-up, robustness and response rapidity are achieved; The results of the implementation of the suggested controls on DSP as HIL confirm the results obtained in Simulink. Accordingly, the effectiveness of this control has been verified.