In this paper, an adaptive neural phaselocked loop (ANPLL) based on adaptive linear neuron is proposed for gridconnected doubly fed induction generator (DFIG) synchronization. The proposed ANPLL architecture comprises three stages, namely, the frequency of polluted and distorted grid voltages is tracked online; the grid voltages are filtered, and the voltage vector amplitude is detected; the phase angle is estimated. First, the ANPLL architecture is implemented and applied to a real threephase power supply. Thereafter, the performances and robustness of the new ANPLL under voltage sag and twophase faults are compared with those of conventional PLL. Finally, an application of the suggested ANPLL in the gridconnected DFIGdecoupled control strategy is conducted. Experimental results prove the good performances of the new ANPLL in gridconnected DFIG synchronization.
NOMENCLATURE
v_{as}
,
v_{bs}
,
v_{cs}
,
v_{ar}
,
v_{br}
,
v_{cr}
Stator and rotor
a
,
b
,
c
phase voltages.
i_{as}
,
i_{bs}
,
i_{cs}
,
i_{ar}
,
i_{br}
,
i_{cr}
Stator and rotor
a
,
b
,
c
phase currents.
U_{g}
Grid voltage vector amplitude.
V_{ds}
,
V_{qs}
,
V_{dr}
,
V_{qr}
Stator and rotor
d
–
q
voltages.
I_{ds}
,
I_{qs}
,
I_{dr}
,
I_{qr}
Stator and rotor
d
–
q
currents.
φ_{ds}
,
φ_{qs}
,
φ_{dr}
,
φ_{qr}
Stator and rotor
d
–
q
flux.
L_{s}
,
L_{r}
Stator and rotor cyclic inductances.
M
Mutual inductance.
R_{s}
,
R_{r}
Stator and rotor resistances.
T_{s}
,
T_{r}
Stator and rotor time constants.
σ
=1–
M
^{2}
/(
L_{s}L_{r}
) Leakage factor.
T_{em}
Electromagnetic torque.
p
Number of pole pairs.
ω_{s}
,
ω
,
ω_{r}
Synchronous, rotor, and slip speeds.
P
,
Q
Active and reactive powers.
s
,
r
Subscripts indicating stator and rotor.
d
,
q
Synchronous reference frame.
T_{e}
Sampling period.
I. INTRODUCTION
Doubly fed induction generator (DFIG) is highly attractive for wind energy generation, in which this generator is driven by wind turbine, and its stator is directly connected to grid. DFIG rotor winding is connected to a backtoback power converter that provides variablefrequency rotor voltage
[1]

[3]
. DFIGbased variable speed wind turbines have numerous advantages
[4]
,
[5]
. First, the maximal mechanical power attainable from wind can be extracted and converted to fixedfrequency electric power by adjusting DFIG speed and electromagnetic torque. Second, only a fraction of the nominal electric power passes through the power converters, thus reducing its loss and cost. Third, stator active and reactive powers can be independently controlled.
Conventional control system of DFIGs is based on statorfluxoriented vector control
[6]

[9]
. The proper synchronization with the reference grid is one of the most important aspects to consider in gridconnected DFIG control. The most widely accepted solutions to provide this synchronization are the phaselocked loop (PLL) techniques
[10]
. In conventional control strategies of DFIG, the amplitude, frequency, and phase angle of positivesequence grid voltages are necessary. These quantities are mainly used for synchronization of the system output variables, power flux calculations, or transformation of state variables into rotating reference frame coordinates
[11]
.
The most used technique for gridconnected converter synchronization is the conventional threephase PLL based on synchronous reference frame (SRF). This technique uses Concordia’s and Park’s transformations to translate the threephase voltage vector from the natural reference frame to the rotating one. Conventional PLL technique provides acceptable results under ideal utility conditions. However, this technique is inefficient in the presence of unbalanced grid voltages
[10]
,
[11]
. To overcome this limitation, several PLL algorithms with different characteristics have been developed and presented in the literature recently. A PLL based on adaptive linear optimal filter technique was presented in
[11]
. The authors in
[12]
proposed a filteredsequence PLL structure using Park transformation and moving average filters. A synchronization method derived from the standard PLL based on
pq
theory with a control model using standard
q
PLL structure was provided in
[13]
. A selective harmonic detection system based on threephase cascaded delayed signal cancellation PLL was developed in
[14]
. A PLL based on variable sampling period concept, which allows the automatic adjustment of sampling frequency, was proposed in
[15]
. In
[16]
, the authors proposed an adaptive SRFPLL that rejects voltage disturbances by using several adaptive infiniteimpulseresponse notch filters. Another adaptive PLL structure based on adaptively adjusting the gain of frequency estimation loop was developed in
[17]
to minimize false frequency transients. In
[18]
, a generalized delayed signal cancellation PLL method was proposed. In
[19]
, a frequencylocked loop dual secondorder generalized integrator based on two adaptive filters was implemented on a stationary reference frame.
PLL performances depend on the computational cost of the used algorithms and their immunity to faults. To improve the robustness of the PLL architecture without increasing the computational cost, a new adaptive neural PLL (ANPLL) for gridconnected DFIG synchronization is developed in this study. The proposed ANPLL architecture is based on adaptive linear neuron (ADALINE) networks, which are successfully applied to several fields, such as network frequency tracking
[20]
,
[21]
, current harmonic estimation
[22]
, and induction motor parameter identification
[23]
,
[24]
. The main advantages of the proposed ANPLL are its accuracy, robustness, and adaptive structure. This ANPLL can accurately estimate the frequency in polluted and distorted utility conditions to filter grid voltages and to reconstitute the voltage vector amplitude. The phase angle of power supply is detected using a unitary threephase system obtained from the grid voltage positive sequences.
The remaining of this paper is divided into seven sections. Section II presents the gridconnected DFIG model and decoupled
P
–
Q
control strategy. Section III provides voltage frequency estimation using pseudosquare ADALINE in the presence of harmonic distortion. Section IV demonstrates grid voltage filtering by ADALINE and PLL for phase angle estimation. Section V elucidates the performance comparison between the proposed ANPLL and the conventional PLL in severe utility conditions. Section VI discusses an application of the new ANPLL in the decoupled
P
–
Q
control scheme of the gridconnected DFIG. Finally, Section VII concludes.
II. MODELING AND DECOUPLING P–Q CONTROL OF THE GRIDCONNECTED DFIG
 A. Modeling of the DFIG
In
d
–
q
Park reference frame, the DFIG electric equations can be written as follows:
with
The stator and rotor angular speeds are linked by the following relationship:
The DFIG electromagnetic torque is expressed by the stator flux and the rotor currents as follows:
Finally, the stator and rotor active and reactive powers can be written as follows:
 B. Decoupled P–Q Control of the DFIG
To simplify Equation (4), as well as the DFIG control, a stator flux orientation according to
d
axis is chosen, that is,
φ_{ds}
=
φ_{s}
and
φ_{qs}
=0
[2]
,
[5]
. Equation (4) then becomes
By choosing
d
–
q
Park reference frame related to the stator flux and by neglecting stator resistances, (1) becomes
By replacing
φ_{dr}
and
φ_{qr}
in (7.c) and (7.d),
The stator active and reactive powers can be reconstructed from the rotor currents and stator flux as follows
[3]
,
[9]
:
Equation (6) indicates that the stator flux orientation according to
d
axis permits to obtain an electromagnetic torque; therefore, the stator active power is proportional to
q
axis rotor current. The stator reactive power is proportional to
d
axis rotor current with a constant imposed by the grid.
The stator powers can be controlled independently, as confirmed by the DFIG model given by (8). Each rotor current can be regulated with its own controller. To perform independent control, two proportional–integral (PI) controllers are used. The block diagram of the rotor current regulation is presented in
Fig. 1
.
Block diagram of the rotor current control.
III. PSEUDOSQUARE ADALINE FOR VOLTAGE FREQUENCY ESTIMATION
In this section, the required objective is to estimate online the fundamental frequency of a sinusoidal voltage corrupted by noise and harmonic distortions. This objective is achieved by a pseudosquare ADALINE
[21]
.
ADALINE was introduced for frequency estimation
[20]
. This approach has been used to identify the voltage parameters written as
where
A_{n}
,
ω_{n}
, and
φ_{n}
are the amplitude, pulsation, and phase of
n^{th}
term, respectively. The recursive expression of
v
(
k
) can be deduced as follows:
If the harmonics are neglected, the voltage signal
v
(
k
) can be rewritten as
Fig. 2
shows that by tacking the vector
X
(
k
)=[
v
(
k
–1)
v
(
k
–2)]
^{T}
as input of ADALINE, after convergence, its weight vector
W
(
k
)=[
w
_{1}
(
k
)
w
_{2}
(
k
)] will adapt and converge toward the vector
R
(
k
)=[2cos(
ω
_{1}
(
k
)
T_{e}
) –1]. The least mean square algorithm with the learning rate
η
is used for weight training
[20]
–
[24]
.
ADALINE for frequency tracking.
ADALINE weight vector
W
(
k
)=[
w
_{1}
(
k
)
w
_{2}
(
k
)] is recursively updated as follows:
where
X
(
k
)=[
v
(
k
–1)
v
(
k
–2)] is the input vector,
e
(
k
)=
v
(
k
)–
v_{est}
(
k
) is the estimation error,
η
is the learning rate, and
ε
is a small value used to avoid division by zero if
X
^{T}
(
k
)
X
(
k
)=0.
To prove the stability of the frequency estimator (ADALINE), Lyapunov function candidate for the frequency estimator (13) is used. This function is selected as
where
is ADALINE estimation error, which is defined as
Lyapunov’s convergence criterion must be satisfied, such that
where Δ
V
(
k
) is the change in the Lyapunov function. This change is given by
By using the frequency estimator error dynamics, which can be derived using (15), with the update law (13), Δ
V
(
k
) can be evaluated as
Assuming that
ε
>0 and 0<
η
<2, the bracketed term in (18) is negative. Consequently, the stability condition in (17) is satisfied, as well as the following convergence properties:
where
R
_{0}
is the vector obtained at the perfect convergence of the estimator. According to (19), the augmented error is monotonically nonincreasing; therefore, the convergence is guaranteed, and the weight
w
_{1}
will be converged to 2cos(
ω
_{1}
(
k
)
T_{e}
). At each iteration, the voltage signal frequency can hence be reconstructed online in the following way:
A main advantage of this method is its immunity to the voltage signal amplitude and phase variation or disturbance. A proof of weight convergence of ADALINE can be found in
[20]
.
However, the sampling period
T_{e}
greatly influences the performances of this approach. The estimated frequency
f
_{1}
depends on the sampling period
T_{e}
. In the presence of harmonics, the function
arccos
in (20) is sensitive to weight variation.
Fig. 3
shows the weight value
w
_{1}
according to
T_{e}
for a 50 Hz grid frequency. This figure indicates that
T_{e}
=5 ms represents a good choice because it corresponds to
w
_{1}
=0, which is the center of the range [+2, –2].
Fig. 4
shows the relationship between the frequency and the weight
w
_{1}
for various
T_{e}
values. The maximum variation of the weight is obtained with an adequate sampling period
T_{e}
=1/4
f
_{1}
for
w
_{1}
=0. An example is delivered for
f
_{1}
=50 Hz in this figure. Consequently, the sampling period of
T_{e}
=1/4
f
_{1}
is chosen to maximize the dynamics and ensure the system stability. The choice of
T_{e}
=1/4
f
_{1}
removes a part of the existing harmonics in the voltage. In our case, all the frequencies superior to 100 Hz will be eliminated for
T_{e}
=5 ms.
T_{e} influence on the weight w_{1} convergence value.
Observable frequency as a function of w_{1} for different values of T_{e}.
In
[21]
, ADALINE was concluded to be inadequate in the presence of harmonics. To improve the frequency estimation performance in polluted and distorted voltages, an alternative of this approach is proposed. Premultiplication of
v
(
k
) with
v
(
k
–
D
) is conducted before performing calculations to accentuate the difference between two signals in close frequencies over one period, where D is the number of the delayed sampling periods. Thus, the new voltage signal
V
(
k
) at ADALINE input is
with
α
=cos(
ω
_{1}
DT_{e}
) and
β
=sin(
ω
_{1}
DT_{e}
). If
T_{e}
=1/(4
f
_{1}
)=2.5 ms and
D
=
d
/
T_{e}
, with
d
selected to be equal to
T
/4=5 ms (
f
=50 Hz),
α
becomes negligible compared with
β
for frequencies close to 50 Hz. Thus, the voltage signal
V
(
k
) can be written in the following form:
By using ADALINE and following the same procedure as illustrated in
Fig. 2
, the polluted and distorted voltage frequencies can be estimated from the weight
w
_{1}
. The principle scheme is illustrated in
Fig. 5
. This frequency will be used in the grid voltage filtering process developed in the following section.
Frequency estimator based on the pseudosquare ADALINE.
IV. ADALINE FOR GRID VOLTAGE FILTERING AND PLL FOR PHASE ANGLE DETECTION
 A. ADALINE for Grid Voltage Filtering
A grid voltage filtering using ADALINE networks is presented. The idea is to conduct a suitable decomposition of the measured voltage and estimate its positivesequence component. Thereafter, this component will be transformed in an adequate form to be learned by ADALINE.
The proposed filtering method applied to the phase
a
is developed. This methodology can be easily generalized to the phases
b
and
c
. The measured grid voltage contains a fundamental component and harmonics. In discrete form, the voltage
v_{a}
(
k
) can be written as follows:
where
V_{an}
is the root mean square value of
n^{th}
term, with
ω_{n}
as its pulsation and
φ_{n}
as its phase. The filtering process of this voltage consists of extracting the positivesequence component. After filtering, (23) becomes
This equation can also be written in the following explicit form:
Thus, (25) can be expressed in vectorial notation as follows:
with
One ADALINE with two adaptive weights is able to estimate (26).
X
(
k
) represents the input vector composed of two generated sine waves with unity amplitude and frequency
f
_{1}
=
ω
_{1}
/2
π
.
W_{a}^{T}
represents the weight vector. The voltage fundamental frequency
f
_{1}
is obtained using the previously developed strategy (Section III).
For the phases
b
and
c
, the obtained vectorial notations are respectively given as follows:
with
After filtering, sinusoidal threephase voltages are obtained. The resulting amplitudes are equal to the fundamental amplitudes of each phase. These filtered voltages can be written in the following form:
The filtering scheme of the grid voltages
v_{a}
,
v_{b}
, and
v_{c}
using the proposed strategy is shown in
Fig. 6
. These voltages will be used in the following subsection for phase angle detection.
ADALINE for grid voltage filtering.
 B. PLL for Phase Angle Detection
Before detecting the phase angle of the filtered voltages using a PLL, a new unitary threephase system is applied to (30). Each voltage is divided by its amplitude. Consequently, a sinusoidal and balanced threephase system with unit amplitude is obtained. This new system is independent on the grid voltage levels and is in phase. By applying this principle to (30), a sinusoidal and balanced unitary threephase system is computed as follows:
with
The grid voltage amplitudes are detected by using an envelope detector available in MATLAB–Simulink library. The amplitude detector algorithm aims to detect the periodic signal amplitude. This detection is based on a switch block that sends the greater value of that obtained at times
kT_{e}
and (
k
–1)
T_{e}
to the output. In this work, the proposed envelope detector scheme is slightly extended for negative signals. The block diagram of the unitary threephase system determination and the amplitude detection algorithm schemes are shown in
Fig. 7
.
(a) Unitary threephase system determination and (b) amplitude detection algorithm of the grid voltages.
Thereafter, the obtained threephase system (31) can be applied to a PLL to determine accurately the phase angle. The principle diagram of the PLL is presented in
Fig. 8
. The PLL uses a fundamental property of Park’s transformation
[11]
. If the estimated pulsation
ω
_{est1}
used in the transformation is equal to the balanced threephase system pulsation
ω
_{1}
, then
d
 and
q
axis components are constant. The obtained sinusoidal threephase system (31) is translated via Concordia’s transformation. The estimated angle
θ
_{est1}
of Park’s rotation is performed by integrating
ω
_{est1}
obtained by PI controller. The pulsation
ω
_{est1}
must be identical to
v_{abcr}
(
θ
_{1}
) pulsation. The amplitude of the controlled
V_{dr}
determines the shift between
V_{r}
value and sin(
θ
_{1}
). The difference in the phase will be controlled by
V^{*}_{dr}
. The PLL will be locked when the estimated angle
θ
_{est1}
is equal to
θ
_{1}
. This condition is realized if
V^{*}_{dr}
is maintained equal to zero. To achieve good performances by this PLL, the threephase system must be sinusoidal and balanced. To this end, the voltages are filtered and transformed into a unitary threephase system. PI parameters are calculated by considering the linearized model for small variations in
θ
_{1}
. As the grid voltage vector is maintained according to
q
axis, its amplitude can be estimated from the detected amplitudes of
a
,
b
, and
c
phases in the following way (given as a negative quantity):
PLL principle scheme for phase angle detection from the unitary threephase system.
The block diagram of the suggested ANPLL strategy is shown in
Fig. 9
. The blocks “Amplitude” (described in
Fig. 7
) divide the input voltages by their amplitudes.
Complete scheme principle of the proposed ANPLL.
V. EXPERIMENTAL VERIFICATION OF THE PROPOSED ANPLL
To verify and compare the suggested ANPLL performance with the conventional PLL, an experiment is conducted. A DS1104 dSPACE board based on TMS320F240 floating point DSP is used. The proposed ANPLL and the conventional PLL algorithms are implemented under MATLAB–Simulink with a sampling period of 0.1 ms. In this section, the DFIG wind turbine is not operated. The used conventional PLL is based on SRF
[11]
, as described in
Fig. 8
. The measured grid voltages are directly applied to this conventional PLL; therefore, no adaptive filter interfacing scheme is inserted at its input.
An experimental comparative study between the ANPLL and the conventional PLL is presented. The estimated quantities, such as voltage vector amplitude, frequency, and phase angle, are considered as comparison quantities. The measured grid voltages, filtered voltages, and unitary threephase system are shown to analyze the ANPLL operation. The learning rates of the used ADALINE networks in the ANPLL, ensuring an optimal speed of weight convergence, are experimentally adjusted. For the pseudosquare ADALINE, the learning rate is set to 0.04; for the adaptive filtering, the learning rate is set to 0.01. PI parameters in the PLL are calculated to obtain a response time
t_{r}
=10 ms, a damping coefficient
z
=1, and a natural pulsation
ω_{n}
=4.5 rad/s. Two disturbances, namely, voltage sag and twophase fault, are considered. In the experiment, a performance analysis of the ANPLL in normal operating conditions (without faults) is first conducted. A comparative study between the ANPLL and the conventional PLL under severe conditions is then performed. In this study, the grid voltage frequency is unaffected. Only variations in the grid voltage amplitudes are created.
Fig. 10
shows ANPLL performances under normal operating conditions. The filtered grid voltages [
Fig. 10
(b)] are in phase with the real measured grid voltages [
Fig. 10
(a)]. By dividing each filtered voltage by its detected amplitude, a sinusoidal and balanced threephase system is obtained with unit amplitude and in phase with the grid voltages [
Fig. 10
(c)]. Thereafter, the detected maximal amplitudes are exploited to estimate the voltage vector amplitude
U_{gest}
. As shown in
Fig. 10
d, the amplitude
U_{gest}
is estimated with high precision and low oscillations caused by frequency fluctuation. This frequency fluctuation, in the grid voltage, affects the calculation in Park’s transformation. Hence, small fluctuations are obtained in the calculated
d
 and
q
axis components of the grid voltage. The pseudosquare ADALINE conceived to estimate the utility frequency in distortion voltages shows good performances [
Fig. 10
(e)]. The minor oscillations observed in the estimated frequency are due to the utility frequency fluctuation (±0.2 Hz), which is acceptable because the tolerance interval in this condition is ±0.5 Hz. The obtained unitary threephase system, which is given in
Fig. 10
c, is used to detect the phase angle by a PLL.
Fig. 10
(f) reveals that the phase angle is well estimated. This result proves the good performance of the proposed ANPLL strategy under normal operating conditions.
ANPLL performances in normal operating conditions. (a) Grid voltages. (b) Filtered grid voltages. (c) Unitary threephase system. (d) Voltage vector amplitude. (e) Frequency.(f) Phase angle.
Fig. 11
shows the performance comparison between the conventional PLL and the ANPLL under 50% voltage sag. At t=0.63 s, a voltage sag appears [
Fig. 11
(a)], which is generated by multiplying the voltage sensor gains of the phases
a
,
b
, and
c
by 0.5 at time 0.63 s. ADALINEbased filter follows perfectly the grid voltages change in steady state. Only 0.1 s is needed to estimate accurately the positivesequence components after the disturbance appearance [
Fig. 11
(b)]. The unitary threephase system has also been reconstructed in 0.1 s after disturbance starting [
Fig. 11
(c)]. The voltage vector amplitude is well estimated with the ANPLL compared with the conventional PLL [
Fig. 11
(d)]. However, a transient state is observed in the amplitude estimation in ANPLL. This transient state is due to ADALINE weight adaptation and learning process following the grid voltage change.
Fig. 11
(d) shows that voltage sag appears rapidly in the conventional PLL compared with the ANPLL. However, the main advantage of the proposed ANPLL is clearly shown in the steady state operation, in which the ANPLL estimates better the grid voltage parameters than the conventional PLL does. To improve the transient state of the proposed ANPLL, the sampling period
T_{e}
used in the implementation must be reduced because according to (13), ADALINE weight learning is performed by iterations. Therefore, using lower sampling period leads to fast learning, and the transient state will be reduced. Nevertheless, the estimated utility frequency from the conventional PLL has considerable fluctuation compared with the signal obtained from the ANPLL [
Fig. 11
(e)], which remains insensitive to the disturbance. As shown in
Fig. 11
(f), the estimated phase angle from the conventional PLL is distorted because the angle is directly calculated from the estimated frequency.
Comparison between the conventional PLL and the ANPLL under 50% voltage sag in grid voltages. (a) Grid voltages. (b) Filtered grid voltages. (c) Unitary threephase system. (d) Voltage vector amplitude. (e) Frequency. (f) Phase angle.
Fig. 12
shows the performances under twophase faults. At t=0.925 s, a voltage sag of 50% appears in the phases
a
and
b
[
Fig. 12
(a)]. This voltage sag is also created by multiplying the voltage sensor gains of the phases
a
and
b
by 0.5 at time 0.925 s. The filtered grid voltages and the unitary threephase system are accurately estimated as shown in
Figs. 12
b and
12
c, respectively. This result confirms the ability of the proposed method in extracting a sinusoidal and balanced unitary threephase system from unbalanced and distorted threephase voltages. In
Fig. 12
(d), the estimated voltage vector amplitude from the conventional PLL presents a considerable distortion, especially during fault conditions, compared with the signal provided by the ANPLL. Moreover, the estimated utility frequency and the phase angle performed by the ANPLL are insensitive to the fault, as shown in
Figs. 12
(e) and
12
(f), respectively.
Comparison between the conventional PLL and the ANPLL under a twophase fault: (a) grid voltages, (b) filtered grid voltages, (c) unitary threephase system, (d) voltage vector amplitude, (e) frequency, and (f) phase angle.
VI. EXPERIMENTAL VALIDATION OF THE ANPLL IN THE GRIDCONNECTED DFIG DECOUPLED P–Q CONTROL
To experimentally validate the decoupled
P
–
Q
control of the DFIG including the proposed ANPLL, a test bench, which is realized in our laboratory, is used. DFIG control is conducted through a PWM converter connected to its rotor and feed from a battery system. The decoupled
P
–
Q
control of the DFIG is implemented in the same dSPACE board used in the previous experiment. The control algorithm is implemented under MATLAB–Simulink with a sampling period of 0.25 ms and a
Runge–Kutta
(ode4) method resolution. The principle scheme of the experimental set up is shown in
Fig 13
. The parameters and characteristics of the controlled DFIG are presented in Appendix. In this section, the proposed ANPLL associated with the DFIG control strategy is validated only in normal operating conditions (no frequency variations and no grid voltage disturbances).
Implementation scheme of the gridconnected DFIG decoupled P–Q control strategy using the proposed ANPLL.
Two tests are conducted. The first test is performed at negative stator active power (
P_{s}
<0), and the second test is performed at negative stator reactive power (
Q_{s}
<0). These two tests are preceded by a test at zero stator powers (
P_{s}
=0,
Q_{s}
=0). During these tests, the DFIG is driven by a DC motor operating in open loop control. Hence, the rotor speed is likely changed when the DFIG provides stator power to the grid.
 A. Test at Ps=0 and Qs=0
Figs. 14
and
15
illustrate the obtained experimental results at zero stator active and reactive powers of the controlled DFIG, respectively.
ANPLL performances: (a) stator voltage pulsation, (b) grid voltage vector amplitude, and (c) phase angle.
Decoupling P–Q control of the DFIG at P_{s}=0 and Q_{s}=0: (a) stator active and reactive powers, (b) rotor speed, (c) rotor voltages, (d) rotor currents, and (e) stator voltage and current of the phase a.
The ANPLL performances are shown in
Fig. 14
. The ANPLL estimates accurately the pulsation [
Fig. 14
(a)], amplitude [
Fig. 14
(b)], and phase angle [
Fig. 14
(c)] of the grid voltage vector. These variables are used directly in the decoupled
P
–
Q
control of the DFIG. The stator phase voltage of the DFIG is set to 110 V, which is the half of the rated voltage.
The obtained results from the decoupled P–Q control of the DFIG at zero stator active and reactive powers are illustrated in
Fig. 15
. Ps and Qs are regulated to zero, as shown in
Fig. 15
(a). In this test, the DFIG is driven at 1530 rpm [
Fig. 15
(b)]. To obtain a zero stator power, the controllers apply a rotor voltage [
Fig. 15
(c)]. Hence, the quadratic rotor current (Iqr) is set to zero (therefore, Ps=0), and the direct rotor current (Idr) is maintained at a sufficient value for canceling the stator flux [
Fig. 15
(d)]. As a result, the stator currents become null [
Fig. 15
(e)].
 B. Test at Ps<0 and Qs=0
This test consists of applying a negative step of the active power reference (Psref<0) to the DFIG stator to provide an active power to the grid.
Fig. 16
a shows that Ps follows perfectly the reference, whereas Qs is set to zero. The rotor speed decreased from 1530 rpm to 1430 rpm because of the resisting torque applied by the DFIG to the DC motor (
Fig. 16
b).
Fig. 16
c shows the rotor voltages calculated by the controllers to maintain Qs=0 and Ps=−1 kW.
Fig. 16
d illustrates that the sudden change in the quadratic rotor current (Iqr) does not affect the direct rotor current (Idr), which demonstrates that d–qaxis control is perfectly decoupled. The stator voltage and current of the phase a are shown in
Fig. 16
e. The current and voltage are in the phase opposition, which corresponds to Ps<0 and Qs=0.
Decoupling P–Q control of the DFIG at P_{s}<0 and Q_{s}=0: (a) stator active and reactive powers, (b) rotor speed, (c) rotor voltages, (d) rotor currents, and (e) v_{as} and i_{as} at P_{s}<0 and Q_{s}=0.
 C. Test at Qs<0 and Ps=0
This test is performed for a negative step in the reactive power reference
Q_{s}
<0 and
P_{s}
=0.
Fig. 17
a shows that the stator reactive power follows perfectly the reference (
Q
_{sref}
=−500 VAR), whereas the stator active power is set to zero. The rotor speed of the DFIG decreases slightly when
Q_{s}
<0 (
Fig. 17
b).
Fig. 17
c gives the rotor voltages calculated by the controllers to obtain
P_{s}
=0 and
Q_{s}
=−500 VAR. The rotor currents
I_{dr}
and
I_{qr}
are illustrated in
Fig. 17
d, where a perfect decoupling can be observed in the current control. The current
I_{qr}
is set to zero, whereas the current
I_{dr}
increases to −11 A at
Q_{s}
=−500 VAR. The stator voltage and current of the phase a are given in
Fig. 17
e. This figure reveals that the current and voltage are in quadratic, which corresponds to
P_{s}
=0 and
Q_{s}
<0.
Decoupling P–Q control of the DFIG at P_{s}=0 and Q_{s}<0: (a) stator active and reactive powers, (b) rotor speed, (c) rotor voltages, (d) rotor currents, and (e) v_{as} and i_{as} at P_{s}<0 and Q_{s}<0.
In the illustrated results, lower ripples of the currents and powers are observed. The signal quality can be achieved by increasing the PWM frequency, decreasing the sampling period
T_{e}
, and improving the accuracy of different sensors (current, voltage, speed sensors, etc.).
VII. CONCLUSIONS
In this paper, an ANPLL based on ADALINE for gridconnected DFIG control is proposed for the voltage vector amplitude, frequency, and phase angle estimation as an alternative to conventional PLL. The ANPLL architecture is implemented using the dSPACE board and applied to a real power supply to prove its efficiency. A comparative experimental study between the proposed ANPLL and the conventional PLL is also performed. According to the obtained experimental results, the proposed ANPLL improves the robustness and steady state estimation performances. Hence, ANPLL is a suitable synchronization system under severe utility conditions. Finally, experimental validation of the DFIG decoupled
P

Q
control using the new ANPLL is conducted. The experimental results demonstrate the good performances of the ANPLL included in the decoupled
P
–
Q
control scheme of the DFIG. As future work, other experiments can be accomplished to test the proposed ANPLL in DFIG control connected to disturbed grid voltages.
BIO
Ali Bechouche was born in TiziOuzou, Algeria on December 09, 1982. He received Engineer, Magister, and Ph.D. degrees in electrical engineering from the Mouloud Mammeri University of TiziOuzou, TiziOuzou, Algeria in 2007, 2009, and 2013, respectively. He is currently an Associate Professor in the Department of Electrical Engineering, Mouloud Mammeri University of TiziOuzou. His research interests include electrical drives and advanced techniques applied to wind energy conversion systems.
Djaffar Ould Abdeslam was born in TiziOuzou, Algeria on April 20, 1976. He received M.Sc. degree in electrical engineering from the University of FrancheComté, Besançon, France in 2002 and Ph.D. degree from the University of HauteAlsace, Mulhouse, France in 2005. He is currently an Associate Professor in the University of HauteAlsace. His research interest includes artificial neural networks applied to power active filters and power electronics.
Tahar OtmaneCherif was born in TiziOuzou, Algeria on February 20, 1958. He received Magister and Ph.D. degrees in Electrical Engineering from the Mouloud Mammeri University of TiziOuzou, TiziOuzou, Algeria in 1994 and 2008, respectively. He is currently an Associate Professor in the Department of Electrical Engineering, Mouloud Mammeri University of TiziOuzou. His research interests include electrical machines and wind energy conversion systems.
Hamid Seddiki was born in TiziOuzou, Algeria on March 21, 1966. He received Engineer, Magister, and Ph.D. degrees in electrical engineering from the Mouloud Mammeri University of TiziOuzou, TiziOuzou, Algeria in 1991, 2000, and 2010, respectively. He received Accreditation to Supervise Research (Habilitation Universitaire) in electrical engineering from the Mouloud Mammeri University of TiziOuzou in 2012. Since 1993, he has been with the Mouloud Mammeri University of TiziOuzou, where he is currently an Associate Professor. His main interests include power electronics and electrical drives.
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