key: cord-0065816-z7ahpes3
authors: Chabani, Mohammed Saci; Benchouia, M. T.; Golea, A.; Becherif, Mohamed
title: Finite-State Predictive Current Control of a Standalone DFIG-Based Wind Power Generation Systems: Simulation and Experimental Analysis
date: 2021-07-15
journal: J Control Autom Electr Syst
DOI: 10.1007/s40313-021-00750-9
sha: d12ba55171c24c61a1a2dac7394362b4812fcfe7
doc_id: 65816
cord_uid: z7ahpes3

This paper presents an improved stator voltage magnitude and frequency control for standalone doubly fed induction generators (DFIGs) based wind power generation systems (WPGSs). The proposed technique uses a simple finite-state predictive current control (FS-PCC). In this control method, the switching vector for the IGBT is selected to minimize the error between the reference value and the predicted value of the rotor current. Moreover, the discrete-time models of (DFIG) are needed to predict the future value of the rotor current for all possible voltage vectors generated by the rotor-side converter (RSC). Since the classic control methods in the literature use inner control loops and are based on pulse width modulation (PWM), this method does not require complex modulation stages and omits the current control loops, which reduces the control requirements. The main objective in a standalone DFIG system is to keep the stator voltage has constant in amplitude and frequency and equal to the reference value, regardless of the changes in rotor speed or load. The proposed control strategy was implemented through a 3 kW DFIG prototype platform-based dSPACE 1104 card. The simulation and experimental results show that the proposed FS-PCC offers excellent reference tracking with less total harmonic distortion (THD) in stator voltages and rotor currents.

Owing to the diminution of fuel fossil reserves and increased concern about CO2 emissions, which can cause a critical climate change, the wind energy systems (WESs) have become attractive and developed rapidly over the last few decades as a clean renewable energy source Kumar, 2016; Soued et al., 2017) . Despite the impacts of Covid-19, the most exclusively published statistics energy has appeared that the total additions of wind energy capacity in 2020 are expected to reach 65 GW, which increased by 8% compared with 2019 (Jaladi et al., 2020; Sadorsky, 2021; Slimane et al., 2020).

B Mohammed Saci Chabani medsaci11@gmail.com 1 LGEB Laboratory, University of Biskra, BP 145, 07000 Biskra, Algeria 2 FCLAB Laboratory, Belfort University, 90010 Belfort Cedex, France Most wind power generation systems (WPGSs) around the world are using the doubly fed induction generators (DFIGs) due to their additional benefits, for instance, wider power capture capability over a large range of wind speeds. Besides, compared to permanent magnet synchronous generators (PMSGs) which require high-power converters, the DFIGs are more economical because they utilized back-toback converters limited at 25%-30% of the DFIG size for supporting a rotor speed variation of ± 30percentage (Dida & Benattous, 2015a , 2015b Ouanjli et al., 2017) .

The field-oriented control (FOC) is an extremely traditional control technique that can be used for DFIG-based systems. This method has been extensively utilized especially in industrial applications. The principle of this method is to transfer the rotor current into a dq rotational reference frame. The FOC technique is implemented through a conventional inner PI controller beside the pulse width modulation (PWM) which can apply the switching sequences to the voltage source converter (VSC). The advantages and disadvantages of this algorithm have been already discussed in many works ( One of the advantages is that the FOC provides accurate current conservation, which is the major goal in control of electrical drives. However, since the PI controllers and the modulation stage are needed for hardware implementation, the complexity and the control system cost will increase.

In the last years, finite-state predictive control (FS-PC) has been successfully used for several applications such as power electronics and electrical drives (Behera & Thakur, 2018; Chebaani et al., 2017; Rahima et al., , 2019; Vazquez et al., 2017) . However, concerning the DFIG-based WECS systems, only an FS-PCC strategy has been described in Mesloub et al. (2016) , where neither addressing the standalone operation mode nor the experimental implementation has been reported.

The major contribution of this article is to adopt the FS-PCC for the standalone DFIGs to overcome the abovementioned disadvantages and improve the control of standalone DFIGs, this control approach seems not been covered yet by the previously published literature in the field of standalone DFIG applications. The idea of FS-PCC is to manipulate the discrete model of DFIG to predict the rotor current by each possible state. The switching state that gives a minimal cost function value will directly select during the next sampling period. Consequently, neither PI current regulators nor pulse width modulators were needed, which is a vital advantage of the proposed FS-PCC when compared with previous control methods. The main challenge of this work is to improve stator voltage and frequency control at variable wind speeds and varying loads. Furthermore, simulation and experimental results are provided in this article. The attain results manifest that the suggested control strategy has perfect transient performance and steady-state response during various load or speed variations.

This article is structured as follows: In Section (II), topology of the system is presented. In Section III, modeling of DFIG and the RSC is presented. The FOC is explained for standalone DFIG is described in Section IV with (FS-PCC). In Section V, simulation and experimental results are extended for various operating conditions. Finally, a conclusion is given in Section VI. Figure 1 shows the configuration of a standalone WPGS integrated DFIG. Two-level voltage source converters with back-to-back structures have been included between the stator and rotor in this topology, which is well recognized as the load side converter (LSC) and (RSC). This paper concerns only the RSC and the standalone DFIG.

The mathematical equations of the DFIG in complex-domain can be defined by referring all the rotor and stator quantities of the DFIG to the stator-windings as ( 

where v s , v r , i s and i r represent the voltage in stator and rotor, the currents in stator and rotor, respectively. Moreover, ψ s , ψ r denote the stator and rotor flux vectors, respectively. R s and R r are the resistances per phase in stator and rotor, respectively. L s , L r are the inductances per phase in stator and rotor, respectively. L m is the mutual inductance, respectively, and L m is the electrical speed. The leakage factor of the DFIG can be defined as

The stator and rotor fluxes relationship can be achieved by the manipulation of (3, 4, 5) as

In this work, the RSC is a two-level (VSC) that has six IGBT power switches intended for applying the FS-PCC method. The structure of the RSC and all rotor voltage vectors is depicted in Fig. 2 . The switching sequences S can be composed as the following equation:

where a e − j2π/3 , S i 1 means S i on, S i means off, and i a, b, c. All rotor voltage vector v is linked to the switching state S by v v dc .S (8) where v dc is the dc-link input voltage that supplies the RSC. Table 1 .

The switching states of the RSC are controlled by the switching pulses Sa, Sb, Sa as follows: 

FOC is applied for the standalone DFIG to achieve the current decoupling control. The stator flux vector is oriented along the d-axis, while the stator voltage vector needs to align along the q-axis to achieve voltage-decoupling control (Chabani et al., 2017) . By forcing, the stator flux ψ sq and stator voltage v sd to be null the orientation are achieved. This leads to a dynamic first-order transfer function with a derivative-time equal to τ s as below:

where stator time constant τ s L s R s , and

That is

The rotor currents can be predicted for all sectors of the rotor voltage, in the proposed FS-PCC algorithm, these predicted rotor currents will contrast with the reference value of rotor current and then are evaluated by a simple cost function. The minimum value of the cost function will reveal the optimal vector rotor voltage which will be applied for the RSC in the next sampling period. 

The prediction algorithm of the rotor current i r is based on the discrete Euler-forward model of the complex rotor current of the DFIG as

T s is the sampling time. Also, the rotor flux is estimated by:

Then, the stator flux can be estimated by using Eq. (6) According to Barra et al., (2016) ; Soued et al., 2017) , the rotor current is predicted through the expression as follows:

where k s

In the actual systems that perform predictive control, a large amount of time calculation is required, and a large amount of retard time introduced during the excitation must be compensated. The time delay compensation of the FS-PCC algorithm must be accomplished by advancing the current prediction two steps ahead (Chebaani et al., 2017; Vazquez et al., 2017) . For instance, supposing that the determined vector will be used at the time (k + 1), and then, it is necessary to predict the current value at (k + 2) time. By moving (15) one time-step forward, the equation of ir (k + 2) can be written as:

For the seven vectors of the rotor voltage which can be produced through the RSC, the rotor current will be predicted at the future sampling time. A cost function is made to evaluate all predicted rotor currents, and it is used as a condition for selecting the best vector of the rotor voltage. The vector of the rotor voltage that minimizes the cost value will choose to use in the next period. The cost function is expressed by the absolute error between the predicted and reference rotor current, as the below equation:

where i * r α (k) and i * rβ (k) are the reference of rotor currents in αβ coordinate frame. Besides, i p r α (k + 2) and i p rβ (k + 2) are the predictive rotor currents. Figure 3 shows the global control scheme of stator voltage and frequency control-based FS-PCC, and the output voltage magnitude in the stator of DFIG is controlled by regulating the d-rotor current (i rd ). While the d-rotor current reference i rd * can be generated after reducing the error between the desired and measured voltage magnitude v an * and v an through a PI (Proportional Integral) controller (Kanojiya, 2012) . The stator of the DFIG is connected in Y-mode; the 

For the standalone DFIG, the system produces electric power as much as the load demand. So, the reference of qrotor current (i rq ) is calculated from the q-stator current (i sq ) as (Abdeddaim & Betka, 2013) :

This proposed FS-PCC is developed to be realized in a fixed αβ rotor reference frame. The Park transformation matrix and the reference rotor currents in dq are transformed to αβ coordinates by:

Finally, to control the output stator frequency at the desired value fs 50 Hz, all the stator quantities must be synchronized with the dq rotating reference frame. Hene, the d-and q-axis of both stator voltages and stator currents are generated by transforming the three-phase stator quantities through the To determine the performance of the proposed control method, the behavior of the controlled system is evaluated during the blow running conditions: Figure 6 (a), (b) illustrates the reference and actual stator voltage amplitude stator phase voltage and rotor phase current. It is easily seen that the stator voltage amplitude has a perfect reference tracking capability for any change in reference value. Both simulation and the experimental show that the stator voltage and the rotor current have good sinusoid waveform due to the application of FS-PCC. The transient behaviors of the applied FS-PCC method for rotor current in the αβ axis are studied. Figure 5a , b presents the reference and measured rotor currents in the αβ axis in the presence of stator voltage steps, It can be noticed that the rotor cur- Fig. 6a , b shows the variation of stator active power and electromagnetic torque of the generator with low ripples when the stator voltage amplitude is varied by increasing and decreasing its value.

To investigate the impact of the load change, which is connected to the stator of DFIG, the load is increased from 2 to 4 kW at 1.7 s and is decreased from 4 to 2 kW at 3.7 s when the DFIG operates with a constant rotor speed of 1450 r/min. The various simulation results and experimental tests are obtained with the proposed FS-PCC strategy under the variation in load value are shown in Figs. 7-8. Figure 7 a and b illustrates the reference and measured stator voltage amplitude, stator current, and rotor current. It is obvious that stator voltage amplitude has been affected by load application, by showing an undershoot, then the amplitude has been recovered quickly because of the regulation loop. Also, the increase and decrease in the stator and rotor current are due to the increase and decrease in load value. Figure 9a and b shows that the stator voltage remains fixed at the desired value of 250 V despite the load variations. Figure 8a and b shows that the variation of stator active power and electromagnetic generator torque is evident due to the load variation. The negative value indicates that the delivered quantity is toward the load.

To reveal the stability of the suggested FS-PCC strategy, the responses of the system are analyzed during emulating, and a different wind gust scenario has been considered. The speed of the DFIG is suddenly decreased from 1450 to 1300 rpm at 1.7 s and increased from 1300 to 1450 rpm at 3.7 s. This test has been done with a fixed load of 2 kW and stator voltage 250 V. The obtained results during this rotor speed Figure 10a and b illustrates the rotational speed, the reference, and actual stator voltage amplitudes, the rotor current. It can be seen that the magnitude is not affected at all and tracks the reference perfectly for the entire period of test, Fig. 11a and b illustrates the rotational speed, the slip angle, stator voltage, and rotor current, it is also seen that the variation of the frequency of rotor current is evident due to the rotor mechanical speed variation. Thus, from zoom (1) and (2), it is observed that the stator voltage frequency remains constant at 50 Hz despite the variation in rotor speed due to the sum of the mechanical and electrical rotor current frequency (Fig. 12 ).

The other important issue in standalone DFIG mode is the power quality since the loads are mostly need balanced and non-polluted stator voltage. Therefore, to evaluate the proposed controller scheme, the power quality of the standalone DFIG system is investigated. The THD of the rotor I ra current and stator voltage V sa is obtained at rotor speed 1450 rpm. In Fig. 13a 

In this paper, a simple and effective FS-PCC algorithm for the stator voltage and frequency control for a standalone DFIG has been developed. The proposed controller does not require an inner PI controller or a complex modulation stage, which greatly simplifies the design process. Moreover, it is easy to implement in the αβ synchronizes rotor reference frame, thereby keeping the proposed control algorithm straightforward for the handling of constraints. Simulation results and experimental tests in a laboratory with a 3 kW DFIG scale setup confirm the proposed control algorithm and show the feasibility and effectiveness of the proposed FS-PCC concerning different operating conditions.

Doubly fed induction machine: Modeling and control for wind energy generation

Optimal tracking and robust power control of the DFIG wind turbine

Implementation of MRAC controller of a DFIG based variable speed grid connected wind turbine

Performance investigation of multi-level inverter for DFIG during grid autoreclosure operation

Design and implementation of high performance field oriented control for grid-connected doubly fed induction generator via hysteresis rotor current controller

Sensorless nonlinear control of wind energy systems with doubly fed induction generator

Finite-control-set predictive current control based real and reactive power control of grid-connected hybrid modular multilevel converter

Optimal tuning of PI controller using PSO optimization for indirect power control for DFIG based wind turbine with MPPT

A new rooted tree optimization algorithm for indirect power control of wind turbine based on a doubly-fed induction generator

Implementation and comparative study of control strategies for an isolated DFIG based WECS

Sliding mode predictive control of induction motor fed by five-leg AC-DC-AC converter with dc-link voltages offset compensation

Predictive control of variable speed wind energy conversion system with multi objective criterions

Doubly-fed induction generator drive system based on maximum power curve searching using fuzzy logic controller

Modeling and control of DFIG through back-to-back five levels converters based on neuro-fuzzy controller

Contribution to the performance improvement of doubly fed induction machine functioning in motor mode by the DTC control

Real-Time simulator of DTC-FOC-based DFIG during voltage dip and LVRT

Method for speed control of DC motor

Wind energy: Trends and enabling technologies

Performance of a vector control for dfig driven by wind turbine: Real time simulation using DS1104 controller board

Dspace DS1104 implementation of a robust nonlinear controller applied for DFIG driven by wind turbine

Predictive DTC schemes with PI regulator and particle swarm optimization for PMSM drive: Comparative simulation and experimental study

High performance active power filter implementation based on predictive current control

Implementation of direct stator voltage control of standalone DFIG based wind energy conversion system

Wind energy for sustainable development: Driving factors and future outlook

Second order sliding mode maximum power point tracking of wind turbine systems based on double fed induction generator

Experimental behaviour analysis for optimally controlled standalone DFIG system

Optimal blade pitch control for enhancing the dynamic performance of wind power plants via metaheuristic optimisers

Model predictive control for power converters and drives: Advances and trends

Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations

See Tables 2 and 3 .