Integral sliding mode control for back-to-back converter of DFIG wind turbine system

: In this study, an integral sliding mode control approach for controlling the power electronics converters of a doubly-fed induction generator (DFIG) wind turbine system is presented. The power electronics interface consists of back-to-back converters. The rotor side converter regulates the active and reactive powers at the DFIG stator through controlling the stator currents. The stator current dynamics, with respect to the rotor voltages, is developed from the conventional equations of the DFIG model. In this control configuration, the knowledge about the rotor currents is not required, which reduces the use of the current measurement sensors. The grid side converter ensures constant dc-link voltage while transferring the power from the DFIG rotor to the grid. The proposed control approach uses a composition of sliding mode and integral parts to improve the overall performance and robustness against parametric variations and uncertainties. A lab-scale DFIG wind turbine system is used to investigate the proposed control approach efficiency under various operating conditions. The experimental results show the effectiveness of the proposed control approach in achieving control objectives to operate the DFIG wind turbine system.


Introduction
The world is facing significant challenges due to the excessive use of fossil fuels. The negative effects on the environment and health are becoming more dangerous. Thus, clean or green energy such as renewable energy is considered as the future of energy sources by many researchers and governments. Wind energy is among the fastest-growing renewable energy sources [1]. In fact, wind energy is now competitive or even cheaper than conventional energy sources [2]. Doubly-fed induction generator (DFIG) is one of the preferred electrical generators used in wind turbines nowadays. It has great features such as variable speed operation and lower cost of power converters, which are typically 30% of the wind turbine ratings [3]. However, it requires complex protection and control schemes. The control objectives of DFIG wind energy systems are precise control of the generated power to maximise the power extraction and dc-link voltage and to optimise the power transfer, under different conditions. Nevertheless, the conventional control methods such as proportional-integral control (PI) control require careful tuning of the gains and accurate knowledge of system parameters, which are not easy tasks in practice. Thus, robust control approaches are the preferred solutions to overcome these drawbacks.
Sliding mode control (SMC) is a robust control approach that deals efficiently with uncertainties. This means that this control method has immunity to uncertainties due to parametric variations and unknown disturbances [4]. This feature is very important in wind energy applications. The control system should act fast to generate the maximum power and eliminate undesired mismatches, disturbances, and uncertainties due to the sudden changes in wind speeds. Different techniques were investigated to improve the SMC practical implementation by reducing the chattering phenomena and at the same time utilising the SMC robustness and disturbance rejection abilities. SMC methods were used in many applications and DFIG wind energy systems as well [5,6]. A terminal SMC, which enables the DFIG system to operate under fault conditions, was presented in [7]. A higher-order SMC, which is capable of operating under unbalances and grid fault conditions, was proposed in [8]. Another interesting SMC approach, which aims to improve the power quality in the grid, was introduced in [9]. This approach uses a super twisting sliding mode disturbance observer. One more recent SMC approach, i.e. based on variable gain super twisting, was presented in [10]. However, these studies use the rotor currents to develop the SMC approach and did not validate their proposed SMC methods experimentally on a real DFIG setup. In [11], the SMC method was used to regulate the DFIG active-reactive powers, at the rotor side converter (RSC), using the rotor currents, which increases the number of sensors for stator and rotor currents measurements. In [12], a tracking error and its integration were used to define the sliding surface of the SMC to control only the stator power of the DFIG at the RSC and the grid side converter (GSC) was not discussed in that study. In [13], a similar control approach was used for the RSC for the rotor speed tracking and the GSC for the dc-link voltage regulation. In both studies, only software simulation was used to validate the proposed controllers. In [14], SMC algorithms for the RSC and GSC of the DFIG wind turbine system, operating under unbalanced grid voltage conditions, were developed and tested by software simulation. In [15], a second-order SMC scheme was used to regulate the stator power of the DFIG through controlling the electromagnetic torque and the direct component of the stator current at the RSC without a discussion about the GSC. The work in [16], verified only by software simulation, is similar to [15], except for varying the control gains, which complicates the control implementation and increases the computation burden. A similar second-order SMC was used in [17] for controlling the power at the GSC of the DFIG system. In [18], a discrete version was implemented to estimate the power reference from the operational conditions. In [19], the stator power regulation, at the RSC, was performed using a simple SMC based on the rotor current, and proportional-integral controllers were used to regulate the dc-link voltage and power control at the GSC.
Development of SMC techniques and applications to DFIG systems is still attracting the attention of the research community due to their features to deal with uncertainties represented by model-based control methods. In [20], SMC was used to control the torque and reactive power by the rotor current components. In [21], the conventional SMC was used for DFIG stator active and reactive power to track desired values through the rotor currents controlled by the RSC, where the dc-link and DFIG models were approximated by a recurrent high-order neural network identifier. In [22], the DFIG stator power is directly controlled by a first-order SMC under all grid conditions. In [23], SMC is combined with feedback linearisation for the overall DFIG grid-connected system. In [24], a high-gain SMC was applied to the DFIG model to control the stator power, where the rotor current is not required in the control implementation. However, there is no discussion about the control at the grid side.
Model predictive control (MPC) was applied for power control in the DFIG system [25][26][27]. These control methods are based on the parameters of the DFIG model, where the controllers are carried out using the nominal parameter values. Therefore, unknown parametric variations can lead to deviations in the predicted power and the MPC is no longer robust against parametric uncertainties.
Concerning rotor current sensorless control, a proportionalresonant controller was used, in [28], for controlling the DFIG stator power through the stator current without requiring the power control loop. Although the obtained results are good, the integration of the generator in the energy system was not discussed. In [29], the H ∞ controller was used for the stator current control as the inner control loop while the outer control loop regulates the stator active-reactive power of DFIG in the wind turbine system. Owing to the size of the closed-loop system, the stability was not studied, and the control method was only tested by simulation at the generator side. In [30], an adaptive SMC for DFIG stator power with sensorless rotor current and constant switching frequency was introduced for the DFIG-based wind energy system. The control method was directly applied to the stator power at the RSC without an analysis of the effect of the GSC.
The objectives of this study are to overcome the aforementioned issues and operate the DFIG wind energy system effectively through controlling the DFIG stator power at the generator side and the dc-link voltage at the grid side. In contrast to the above control methods that use the stator and rotor currents for modelling and power regulation, only the stator currents are used to control the DFIG stator power. By using the stator currents, an additional power control loop can be avoided, and the system parameters information has a lower impact on the control approach. The proposed SMC has an integral action, which ensures a zero-steadystate error while eliminating the effects of uncertainties due to the parametric variations and unknown disturbance. Furthermore, its structure ensures the stability of the closed-loop system. The implementation of the proposed control system requires fewer current sensors, as the rotor currents are no longer required, which reduces the noises in the control loop.

DFIG wind energy system
The DFIG wind energy system is shown in Fig. 1. The main parts of the system are DFIG, GSC, RSC, filter, and the grid. The GSC regulates the dc-link voltage and maintains power exchange to the grid, while RSC regulates the generated power. The filter removes the high-switching frequency components.

DFIG modelling
In the synchronous rotating reference frame (d-q), the DFIG stator and rotor dynamics are represented by [20] where v sd and v sq are the d-q components of the stator voltage, i sd and i sq are the d-q components of the stator current, ϕ sd and ϕ sq are the d-q components of the stator flux, R s is the stator resistance, v rd and v rq are the d-q components of the rotor voltage, i rd and i rq are the d-q components of the rotor current, ϕ rd and ϕ rq are the d-q components of the rotor flux, R r is the rotor resistance, ω s is the synchronous angular speed, ω r is the rotational speed, and s = ω s − ω r /ω s .
Note: z˙= dz/dt is the derivative of variable z. Furthermore, the stator and rotor fluxes are expressed by where L s , L r and L m are the stator inductance, rotor inductance, and mutual inductance, respectively. The stator current dynamics, with respect to the rotor voltages, is carried out from (1) and (2) and given by The dynamics (3) is developed under the assumptions of stator voltage and stator flux alignments, such as DFIG stator power with assumptions (4) are given by The electromagnetic torque of the generator is given by where p is the number of pole pairs of the electric machine. Now, by using the stator flux in (2) and assumptions (4), the electromagnetic torque (6) becomes

Grid modelling
The grid current dynamics in the (d-q) reference frame are where v d and v q are the d-q components of the grid voltage, i d and i q are the d-q components of the grid current, R is the filter resistance, L is the filter inductance, and ω is the angular pulsation. The active power and reactive power at the grid converter output can be approximated using (4) such as The dynamics of the dc-link voltage between the two converters is expressed by where I r is the current at the output of the RSC and I r is the current input to the GSC. Assuming the ideal grid converter, the active power, at both converter sides, is approximated such as The dc-link voltage dynamics (10) can be reorganised using (11) and becomes where a V = (3/2)(V s /V dc * ).

Integral SMC (ISMC) design
The ISMC structure is carried out for a single input-output state model defined by where x is the controlled output, v is the control input, η is the disturbance, and (b, d) are parameters based on the system modelling.
The control objective is to model the system as an integrator under the form where u is the new control input In this study, the proposed ISMC law is under the form where e = x*−x is the tracking error, sgn is the sigmoid function, and S is the sliding surface.
The sliding surface has an integral component and is defined such as [13] The advantage of an integral action in the sliding surface is to ensure a zero-steady state error while eliminating the effects of uncertainties due to the parametric variations and unknown disturbance.
The stability of the system dynamics is guaranteed through the Lyapunov function candidate defined by The time derivate of the function (17) is carried out as It can be noticed, from (18), that the condition of stability is satisfied.

ISMC for RSC
At the RSC, the objective is to control the active-reactive power of the DFIG stator using the d-q components of the stator current. From (5), the stator current reference can be defined from the desired active-reactive stator power (P s * , Q s * ) such as Then, the stator current references (i sd * , i sq * ) are used in the stator current control loop.
Furthermore, the stator current references (i sd * , i sq * ) can be generated from the maximum power point tracking (MPPT) system as shown in Fig. 2. Based on the wind speed v r , the MPPT algorithm provides the speed reference ω mpp , which is used as a reference to control the rotor speed ω r . The PI controller provides the torque reference T em * . Using (7), the current reference i sq * is calculated and used in the control loop. The current reference i sd * can be achieved from (19) by setting a reference for the stator reactive power. As the scope is to develop controllers for stator currents, the MPPT system is not elaborated in this study.
The state model of the stator current (3) under the form (14) is expressed as where u sd and u sq are the new control inputs for d-q components of the stator current, respectively. The ISMC law (15) is used such as The control input (v sd * , v sq * ) is carried out from (20) and (21) The control scheme for the RSC is depicted in Fig. 3. The implementation of the ISMC law (23), at the machine side, requires the knowledge about the rotor speed ω r , which is available by measurements, through the speed encoder, in this work. Techniques of speed estimation can be used and will be investigated in future studies to estimate the rotor speed using stator currents.

ISMC for GSC
At the GSC, the objective is to control the dc-link voltage and the grid current to ensure a smooth power transfer for the DFIG rotor to the grid. The control approach is divided into two main parts, which are inner and outer control loops [10].

Dc-link voltage control
The outer loop control scheme uses the dc-link dynamics to regulate the dc-link voltage. It is regulated to be constant and the controller provides the current reference to the inner loop control.
In the voltage control design, the current I r is considered as an unknown disturbance and omitted from the dc-link voltage dynamics (12), which becomes where u V is the control input.
Although the unknown disturbance is not modelled in the dclink voltage dynamics, it will be compensated by the control system.
The ISMC law for dc-link voltage tracking is given by where e V = V dc * − V dc is the tracking error of the dc-link voltage and the sliding surface is defined, considering (16), by From (24) and (25), the control input is given by The current reference command will be injected into the inner loop control as the reference of the q-component of the grid converter current.

Grid current control
The aim of the inner loop control scheme is to regulate the power transferred from the DFIG through the back-to-back converter by controlling the currents at the GSC output, which are related to the power by (19). The active power is regulated by the q-component of the current, where the reference is generated by the outer control loop. The tracking error dynamics for the GSC current is represented by where u d and u q are the new control inputs for d-q components of the GSC current. The ISMC law for grid converter current tracking is given by From (28) and (29), the control input is given by The control scheme for the GSC is depicted in Fig. 4. The inner control loop is the dc-link voltage controller and the outer control loop is the grid converter currents.

Experimental results
The DFIG laboratory setup that is used to validate the proposed ISMC is shown in Fig. 5. The setup consists of a DFIG coupled with a dynamometer to mimic a variable speed wind turbine [31].
It has a back-to-back converter configuration as shown in Fig. 1. The six pulses, to run the converters, are generated by the pulse width modulation generator (three-arm bridge) with a carrier frequency of 5000 Hz. The experimental setup parameters are summarised in Table 1. Four experiments are conducted to test the proposed ISMC method's effectiveness. These experiments verify the tracking of variable references, robustness against external disturbances, due to the rotor speed variation and dc-link voltage variation, and parametric uncertainties.

Stator current tracking
This experiment is carried out to check the tracking performance of the proposed ISMC approach. It can be clearly observed, from Figs. 6a and b, that the d-q stator current components follow their desired targets and the constant voltage dc-link condition is achieved and well-controlled to the desired value of 300 V as shown in Fig. 6c.

Dc-link voltage tracking under constant stator power
This experiment is conducted to verify the proposed ISMC under variable dc-link voltage. The dc-like follows its references precisely as shown in Fig. 7a. In addition, the power control is not affected by the change in value, and the independent relationship between RSC and GSC is confirmed as shown in Fig. 7b.

Variable speed operation
This experiment is performed to verify the DFIG operation under variable speed as shown in Fig. 8a. The target is to keep a constant stator power, through constant d-q components of the stator currents, and a constant voltage at dc-link under the variable rotor speed operation. This can be verified from the results in Figs. 8b-d for d-stator current, q-stator current, and dc-link voltage, respectively. It can be observed that stator currents are affected by the speed variations but rapidly eliminated by the proposed controllers to reach a zerosteady state error. Similar observation on the voltage tracking at the dc-link.

Parametric variation uncertainties
This experiment is carried out to test the proposed ISMC approach robustness to system parameters mismatch. The target is to control quantities despite the changes in system parameters and rotor speed. The stator resistance is reduced by half and inductance one fifth. Results, in Fig. 9, show that the control target is met under variable rotor speed variation. It can be observed the steady-state error is still maintained at zero level despite the parametric uncertainties.
The experimental results of the proposed ISMC can be compared to the conventional PI control system, developed in [31] for similar applications, where it can be observed that the proposed method has a superior performance with respect to overshoot and tracking. Furthermore, parametric tuning is less complicated compared to the conventional control method.

Conclusions
An ISMC scheme, for stator power control based on only stator currents, is studied through analysis and experimental verification. The proposed control scheme is applied to the DFIG back-to-back converter configuration to ensure smooth power transfer. In this control strategy, the rotor currents are not required to implement the control system, which reduces the number of current sensors. The proposed method is tested under constant and variable rotor speeds and dc-link voltages as well as under the presence of parametric mismatches. The experimental results show satisfactory transients and steady-state operation responses.

Acknowledgments
This work was partially supported by the Canada Foundation for Innovation (CFI) under the project 30527 and the Khalifa University of Science and Technology under Award No. CIRA-2019-049.