1 Introduction

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 (Barra et al., 2016; 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).

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-to-back 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 (Abdeddaim & Betka, 2013; Abdeddaim et al., 2014; Amrane et al., 2016; Bekakra & Ben Attous, 2014; Benamor et al., 2019; Bouchiba et al., 2017; Mensou et al., 2019, 2020; Soued, 2019). 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 above-mentioned 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.

2 Standalone DFIG System Topology

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.

Fig. 1
figure 1

Basic diagram of the standalone WPGSs

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3 Mathematical Models of DFIG and RSC

3.1 DFIG Mathematical Model

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 (Abad et al., 2011; Chikha & Barra, 2016). The stator and rotor voltage equations of the DFIG are

$$ {v}_{{s}} = {R}_{{s}} .{i}_{{s}} + \frac{{d}}{{{dt}}}{\psi }_{{s}} + {j}.\omega _{{m}} .{\psi }_{{s}} $$
(1)
$$ {v}_{{r}} = {R}_{{r}} .{i}_{{r}} + \frac{{d}}{{{dt}}}{\psi }_{{r}} $$
(2)
$$ {\psi }_{{s}} = {L}_{{s}} .{i}_{{s}} + {L}_{{m}} .{i}_{{r}} $$
(3)
$$ {\psi }_{{r}} = {L}_{{r}} .{i}_{{r}} + {L}_{{m}} .{i}_{{s}} {~} $$
(4)

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,\({~\psi }_{{s}}\), \({\psi }_{{r}}\) 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

$$ {\sigma } = 1 - \frac{{{L}_{{m}} ^{2} }}{{{L}_{{s}} .{L}_{{r}} }}{~~} $$
(5)

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

$$ {\psi }_{{s}} = \frac{{{L}_{{s}} }}{{{L}_{{m}} }}.\left( {{\psi }_{{r}} - {\sigma }.{L}_{{r}} .{i}_{{r}} } \right){~} $$
(6)

3.2 RSC Mathematical Model

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:

$$ {S} = \frac{2}{3}.\left( {{S}_{{a}} + {a}.{S}_{{b}} + {a}^{2} .{S}_{{c}} } \right){~} $$
(7)

where \({a} = {e}^{{ - {j}2{\pi }/3}}\), \({S}_{{i}}\) = 1 means \({S}_{{i}}\) on, \(\overline{{{S}_{{i}} }}\) 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.

Fig. 2
figure 2

source inverter; right: voltage vectors

Left: two-level voltage

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Considering the possible eight voltage vi (v0–v7) vectors switching states S (S0–S7) is obtained as shown in Table 1.

Table 1 Voltage vectors and switching states with index number
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The switching states of the RSC are controlled by the switching pulses Sa, Sb, Sa as follows:

$$ {S}_{{a}} = \left\{ {\begin{array}{*{20}c} {1~\rm if~{S}_{{a}} ~\rm on~\rm and~\overline{{{S}_{{a}} }} ~\rm off} \\ {0~\rm if~{S}_{{a}} ~\rm off~\rm and~\overline{{{S}_{{a}} }} \rm on~} \\ \end{array} } \right. $$
(9)
$$ {S}_{{b}} = \left\{ {\begin{array}{*{20}c} {1~\rm if~{S}_{{b}} ~\rm on~\rm and~\overline{{{S}_{{b}} }} ~\rm off} \\ {0~\rm if~{S}_{{b}} ~\rm off~\rm and~\overline{{{S}_{{b}} }} \rm on~} \\ \end{array} } \right. $$
(10)
$$ {S}_{{C}} = \left\{ {\begin{array}{*{20}c} {1~\rm if~{S}_{{c}} ~\rm on~\rm and~\overline{{{S}_{{c}} }} ~\rm off} \\ {0~\rm if~{S}_{{c}} ~\rm off~\rm and~\overline{{{S}_{{c}} }} \rm on~} \\ \end{array} } \right. $$
(11)

4 FOC for Standalone DFIG

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 \({\psi }_{{{sq}}}\) 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 \(\tau _{s}\) as below:

$$ {\psi }_{{{sd}}} = \left| {{\psi }_{{s}} } \right| = \frac{{{L}_{{m}} }}{{{\tau }_{{s}} .{s} + 1}}.{i}_{{{rd}}} ~ $$
(12)

where stator time constant \({\tau }_{{s}} = \frac{{{L}_{{s}} }}{{{R}_{{s}} }}\), and

$$ {\psi }_{{{sq}}} = 0 = {L}_{{s}} .{i}_{{{sq}}} + {L}_{{m}} .{i}_{{{rq}}} {~} $$
(13)

That is

$$ {i}_{{{rq}}} = - \frac{{{L}_{{s}} }}{{{L}_{{m}} }}.{i}_{{{sq}}} {~} $$
(14)

5 Proposed Finite-State Predictive Current Control for Standalone DFIG

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. (Behera & Thakur, 2018; Chebaani et al., 2017; Mesloub et al., 2016).

5.1 Rotor Current Prediction Model

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

$$ \frac{{{di}_{{r}} }}{{{dt}}} \approx \frac{{{i}_{{r}} \left( {{k} + 1} \right) - {i}_{{r}} \left( {K} \right)}}{{{T}_{{s}} }}{~} $$
(15)

\(T_{s}\) is the sampling time. Also, the rotor flux is estimated by:

$$ {\psi }_{{r}} \left( {k} \right) = {\psi }_{{r}} \left( {{k} - 1} \right) + {T}_{{s}} .\left( {{v}_{{r}} \left( {k} \right) - {R}_{{r}} .{i}_{{r}} \left( {k} \right)} \right){~} $$
(16)

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:

$$\begin{aligned} {i}_{{r}} \left( {{k} + 1} \right) &= \left( {1 + \frac{{{T}_{{s}} }}{{{\tau }_{{\sigma }} }}} \right).{i}_{{r}} \left( {k} \right) + \frac{{{T}_{{s}} }}{{{\tau }_{{\sigma }} + {T}_{{s}} }}.\\ &\quad \times\left\{ {\frac{1}{{{R}_{{\sigma }} }}\left[ {\left( {\frac{{{k}_{{s}} }}{{{\tau }_{{s}} }} + {k}_{{s}} {j}\omega _{{m}} } \right){\psi }_{{s}} \left( {k} \right) + {v}_{{r}} \left( {k} \right) - {k}_{{s}} {v}_{{s}} \left( {k} \right)} \right]} \right\}{~}\end{aligned} $$
(17)

where \({k}_{{s}} = \frac{{{L}_{{m}} }}{{{L}_{{s}} }}\) \(~{\tau }_{{s}} = \frac{{{L}_{{s}} }}{{{R}_{{s}} }}\) \({\tau }_{{\sigma }} = ({L}_{{r}} {*\sigma })/{R}_{{\sigma }}\) \(~{R}_{{\sigma }} = {R}_{{r}} - {R}_{{s}} .{k}_{{s}}^{2}\)

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:

$$\begin{aligned} {i}_{{r}} \left( {{k} + 2} \right) &= \left( {1 + \frac{{{T}_{{s}} }}{{{\tau }_{{\sigma }} }}} \right).{i}_{{r}} \left( {{k} + 1} \right) + \frac{{{T}_{{s}} }}{{{\tau }_{{\sigma }} + {T}_{{s}} }}. \\ &\quad\times \left\{ {\frac{1}{{{R}_{{\sigma }} }}\left[ {\left( {\frac{{{k}_{{s}} }}{{{\tau }_{{s}} }} + {k}_{{s}} {j}\omega _{{m}} } \right){\psi }_{{s}} \left( {{k} + 1} \right) + {v}_{{r}} \left( {{k} + 1} \right) - {k}_{{s}} {v}_{{s}} \left( {{k} + 1} \right)} \right]} \right\}{~~} \end{aligned} $$
(18)

5.2 Minimization of the Cost Function

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:

$$ {g} = \left| {{i}_{{{r\alpha }}}^{{*}} \left( {k} \right) - {i}_{{{r\alpha }}}^{{p}} \left( {{k} + 2} \right)} \right| + \left| {{i}_{{{r\beta }}}^{{*}} \left( {k} \right) - {i}_{{{r\beta }}}^{{p}} \left( {{k} + 2} \right)} \right|{~} $$
(19)

where \({i}_{{{r\alpha }}}^{{*}} \left( {k} \right)\) and \({i}_{{{r\beta }}}^{{*}} \left( {k} \right)\) are the reference of rotor currents in \(\alpha \beta\) coordinate frame. Besides, \({i}_{{{r\alpha }}}^{{p}} \left( {{k} + 2} \right)\) and \({i}_{{{r\beta }}}^{{p}} \left( {{k} + 2} \right)\) are the predictive rotor currents.

5.3 Proposed Controller Design

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 \(\left( {{\text{i}}_{{{\text{rd}}}} {\text{~}}^{{\text{*}}} } \right)\) can be generated after reducing the error between the desired and measured voltage magnitude \(\left( {v_{{an}} {\text{~}}^{{\text{*}}} {\text{~}}and{\text{~}}v_{{an}} } \right)\) through a PI (Proportional Integral) controller (Kanojiya, 2012). The stator of the DFIG is connected in Y-mode; the stator voltage magnitude \(\left( {{\text{~}}v_{s} } \right)\) is given by Ahmed et al. (2019) wind energy conversion system.

$$ \left| {{~v}_{{s}} } \right| = {V} = \sqrt {\left( {{~v}_{{{sd}}} ^{2} + {~v}_{{{sq}}} ^{2} } \right)} $$
(20)
Fig. 3
figure 3

Block diagram of FS-PCC of RSC

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

$$ i_{{rq}}^{*} = - \frac{{L_{s} }}{{L_{m} }}i_{{sq}}^{*} $$
(21)

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

$$ \left[ {\begin{array}{*{20}c} {i_{{r\alpha }}^{*} } \\ {i_{{r\beta }}^{*} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {\cos \left( \theta \right)} & {amp; - \sin \left( \theta \right)} \\ {\sin \left( \theta \right)} & {amp;cos\left( \theta \right)} \\ \end{array} } \right].\left[ {\begin{array}{*{20}c} {i_{{rd}}^{*} } \\ {i_{{rq}}^{*} } \\ \end{array} } \right]~ $$
(22)

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 Park transformation with angle (\({{\theta }}_{s}\)), which is obtained by integrating the reference stator frequency \(\omega _{s}\) (314 rad/sec) (Benamor et al., 2019) where

$$ \theta _{{_{r} }} = \theta _{{_{s} }} - \theta _{m} $$
(23)

6 Simulation Results and Experimental Validation

This section presents simulation and experimental examination test results to verify the behavior of the developed FS-PCC. The simulation model has been built in MATLAB/Simulink together with the Sim Power Systems software. Moreover, the experimental results have been obtained using a test platform developed in the laboratory. The characteristics of the DFIG that used for simulation and experimental are reported in Appendix (A). Figure 4 portrays the descriptive diagram and a picture of the experimental prototype setup, and it is composed of a prime mover 3 Kw DC motor, 3 Kw DFIG, 4 Kw/420Ω three-phase resistive load. Semikron module IGBT inverter, dSPACE 1104 control card, a host PC running with MATLAB/Simulink software. The hardware DS1004 card is exploited to implement the FS-PCC strategy, with a sampling time of 100 \(\mu \) s.

Fig. 4
figure 4

A laboratory prototype of the experimental setup

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To determine the performance of the proposed control method, the behavior of the controlled system is evaluated during the blow running conditions:

6.1 Stator Voltage Magnitude Variation

Firstly, the DFIG is driven with a constant speed of 1450 rpm and supplies a fixed 2 Kw of resistive load. To show the dynamic performance of the suggested technique, a variation in the reference of output voltage has been applied. The reference of the stator voltage amplitude has been varied from 200 to 280 V at 1.7 s from 280 to 200 at 3.7 s. The various simulation and the experimental test results are shown in Figs. 5–6. 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 currents are controlled successfully by the proposed FS-PCC method, which achieved a perfect transient response during step change of the stator voltage. Also, 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.

Fig. 5
figure 5

System response under step variation in the reference of stator voltage amplitude. a Simulation results. b Experimental. CH1: reference of stator voltage magnitude (50 V/div), CH2: stator voltage magnitude (50 V/div), CH3: stator phase voltage (200 V/div), CH4: rotor phase current (20A/div)

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Fig. 6 
figure 6

Rotor currents response in αβ under stator voltage change. a Simulation results. b Experimental. CH1: reference and measure rotor current in α axis (10A/div), CH2: reference and measure rotor current in β axis (10A/div)

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6.2 Load Change

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.

Fig. 7
figure 7

System response under load variety.a Simulation results.b Experimental. CH1: reference of stator voltage magnitude (50 V/div), CH2: stator voltage magnitude (50 V/div), CH3: stator phase current (5A/div), CH4: rotor phase current (20A/div)

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Fig. 8 
figure 8

System response under step variation in the reference of stator voltage amplitude. a Simulation results. b Experimental. CH1: reference of stator voltage magnitude (50 V/div), CH2: stator voltage magnitude (50 V/div), CH3: stator active power (1KW/div), CH4: electromagnetic torque (20 N.m/div)

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Fig. 9
figure 9

System response under load variety. a Simulation results. b Experimental. CH1: reference of stator voltage magnitude (50 V/div), CH2: stator voltage amplitude (50 V/div), CH3: stator phase voltage (200 V/div), CH4: rotor phase current (20A/div)

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6.3 Rotational Speed Variation

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 change are shown in Figs. 10–11. 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).

Fig.10 
figure 10

System response under load variety. a Simulation results. b Experimental. CH1: reference of stator voltage magnitude (50 V/div), CH2: stator voltage amplitude (50 V/div), CH3: stator active power (1KW/div), CH4: electromagnetic torque (20 N.m/div)

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Fig. 11
figure 11

System response under rotor speed variety. a Simulation results. b Experimental. CH1: rotor speed (200 rpm/div), CH2: reference of stator voltage amplitude (50 V/div), CH3: stator voltage magnitude (50 V/div), CH4: rotor phase current (20A/div)

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Fig. 12
figure 12

System response under rotor speed variety. a Simulation results. b Experimental. CH1: rotor speed (200 rpm/div), CH2: slip angle (5 rad/div), CH3: stator phase voltage (400 V/div), CH4: rotor phase current (20A/div)

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6.4 THD Assessment

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 and b, the THD of \({I}_{ra}\) is 3.41% for fundamental rotor frequency: \({f}_{r}\)= 1.667 Hz and THD in the stator voltage windings for fundamental rotor frequency 50 Hz is and 4.24%.

Fig. 13
figure 13

Experimental THD analysis. a Phase stator voltage THD. b Phase rotor current THD

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7 Conclusion

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.