MPPT Control of Wind Turbines with Wind Speed
Estimation Using Direct Adaptive Fuzzy-PI Controller
Sanaz Sabzevari, Ali Karimpor, Mohammad bagher Naghibi sistani, Mohammad Monfared
Electrical Engineering Department
Ferdowsi University of Mashhad
Mashhad, Iran
Sanaz.sabzevari@kiaeee.org, karimpor@um.ac.ir, mb-naghibi@um.ac.ir, m.monfared@um.ac.ir
Abstract—This paper presents a maximum power point tracking
(MPPT) technique based on the tip speed ratio control for small
scale wind turbines (WTs). In this paper, artificial neural
network (ANN) with particle swarm optimization (PSO) (ANNPSO) has been trained offline to learn the turbine-characteristic
surface power versus wind and machine speeds and has been
implemented online to estimate the varying wind speed. It is
essential to include a controller that can track the maximum
peak of energy regardless of wind speed changes. Therefore, this
work provides a novel robust direct adaptive fuzzy-PI controller
during MPPT process for permanent magnet synchronous
generator (PMSG) driven by a WT. The proposed method has
successfully reduced the ripples of coefficient of power (Cp)
which is the index of MPPT mode, under wind speed variations
in comparison with conventional controller. Finally, a systematic
analysis is presented as well as simulation results proving the
effectiveness of proposed strategy.
Keywords: Maximum power point tracking (MPPT),
artificial neural network, particle swarm optimization, direct
adaptive fuzzy-PI control, PMSG wind turbine.
I.
INTRODUCTION
Over the past decade, wind energy systems have gained
tremendous attention as one of the most promising renewable
energy sources due to the probable depletion, high costs, and
negative environment impacts of conventional energy sources
[1, 2]. Among renewable energy generation systems, like
those based on wind, photovoltaic, fuel cell, or geothermal
power, wind generators are, in general, more cost effective
than other renewables of the same power rating [3].
Wind turbines are controlled to operate only in a range of
wind speed from cut-in (V cut-in) to cut-out (Vcut-out) speeds.
This paper focuses on the moderate wind speed region from
cut-in speed at which the turbine starts working, to the rated
speed (Vrated), at which the turbine produces its nominal
power. In this region the maximum power point tracking
(MPPT) algorithms are usually employed to maximize the
turbine energy conversion efficiency through regulating the
rotational speed of variable speed wind turbines.
Recently, lots of MPPT algorithms have been proposed by
researchers, which can be categorized into four main groups
based on the specified performance and measurement
requirements: 1) tip speed ratio (TSR) control [4], 2) optimal
torque (OT) control [5], 3) power signal feedback (PSF)
control [6], and 4) perturbation and observation (P&O)
control [7-9]. A detailed performance comparison carried out
in [10] shows that the TSR control presents more advantages
among others. It can be noted that for each wind turbine,
there is a specific ratio called the optimum TSR for which the
extracted power is maximum [1]. In TSR control method as
the wind speed changes instantaneously, it is necessary for
the rotational speed to change accordingly to always maintain
the optimal TSR at all times. Despite its promising features
like fast convergence speed, robustness, simplicity, and no
need for prior training and memory, it needs some kind of
sensors to measure the wind speed. In general, the efficiency
of methods that does not directly measure the wind speed is
lower than compared to other TSR control methods which
directly measure the wind speed. This is due to the fact that
wind changes are not reflected instantaneously and
significantly on the reference signal [5, 10].
In recent years, wind speed sensor-less MPPT controls
have been reported in [11-15], in which the wind speed is
estimated online from the instantaneous inputs [11, 14-15]. In
detail, Bhowmik et al. use a look-up table to approximate the
wind speed; it is estimated online by calculating the roots of a
polynomial of wind turbine power coefficient using an
iterative algorithm [12]. However, real-time calculation of the
polynomial roots may require external memory for highly
accurate
estimation,
therefore,
degrading
system
performance. In [13], Tan and Islam employ a power
equation of an autoregressive statistical model to predict the
wind speed. This method is a time-consuming task and also
the predicted wind speed is not precise for online MPPT
control. Artificial neural networks (ANNs) are beneficial tool
to implement nonlinear complex time-varying input-output
mappings [14].
This paper presents a novel TSR-based MPPT control
algorithm which does not need any information about the
wind speed. Indeed, in the proposed method, the wind speed
sensor is replaced by a very short term wind speed estimator,
which let achieve superior performance compared to other
sensor-less techniques.
In this work, in order to have more precision and
simplicity with less training data, an ANN input-output
mapping with two hidden layers is utilized for wind speed
prediction. The layer’s weights are updated through a particle
swarm optimization (PSO).
Other contribution of this paper is that instead of
conventional PI controllers, a direct adaptive fuzzy-PI
controller is employed which significantly reduces the
dependence on system parameters. Fuzzy controllers are
supposed to work in situations where there is a large
uncertainty or unknown variation in plant parameters and
structures [16, 17]. The main advantages of adaptive fuzzy
control over non-adaptive fuzzy control are: (i) better
performance is usually achieved because the adaptive fuzzy
controller can adjust itself to the changing environment, and
(ii) less information about the plant is required because the
adaptation law can help to learn the dynamics of the plant
during the real-time operation [18].
Figure 1. A Simplified block diagram of the proposed PMSG wind-energy
system [1]
Figure 2. The characteristic of the power coefficient as a function of the tip
speed ratio [10]
This paper is organized as follows. Section 2 explains the
system description of PMSG wind turbine. Section 3
describes ANN-PSO wind speed estimator. Section 4
explains the MPPT control by direct adaptive fuzzy-PI
controller. Section 5 provides the simulation results. Finally,
section 6 concludes the paper.
II.
SYSTEM DESCRIPTION
Fig. 1 shows the scheme of small wind turbine system
based on a permanent magnet synchronous generator
(PMSG). The PMSG is connected to the resistive load
basically through the rectifier and a boost converter. Wind
turbine converts the wind energy into mechanical energy,
which then runs a generator to create electrical energy. The
mechanical power generated by a wind turbine can be
expressed as [19–21]:
1
Pm = 2 ρπR2 Vw3 Cp (λ,β)
Figure 3. Characteristics of the turbine power as a function of the rotor speed
for a different wind speeds [10]
(1)
The turbine power coefficient (Cp) describes the power
extraction efficiency of the wind turbine. It is a nonlinear
function of both the tip speed ratio (λ) and the blade pitch
angle (β). Although its maximum theoretical value is
approximately 0.59, practically it lays between 0.4 and 0.48
[22]. The tip speed ratio is a variable expressing the ratio of
the linear speed of the blade tips to the rotational speed of the
wind turbine [19–21], and can be written as:
λ=
ωm R
Vw
(2)
Figure 4. Block diagram of ANN-PSO based wind speed estimator
In this paper, Cp is defined as [23]:
Cp (λ,β)=0.5176
1
λi
116
λi
1
-
21
-0.4β-5 e λi +0.0068λ
= λ+0.08β -
0.035
β3+1
(3)
(4)
In the present work, due to the premise of a fixed pitch
rotor, the angle (β) is set to zero. Thus, the characteristics of
Cp mainly depend on λ. Fig. 2 shows Cp as a function of λ.
Based on this figure, there is only one optimal point, denoted
by λopt, where Cp is maximum. Continuous operation of the
wind turbine at this point by the tip speed ratio control,
guarantees that it will extract the maximum available power
from the wind at any speed, as shown in Fig. 3.
III.
ANN-PSO WIND SPEED ESTIMATOR
A. Estimation of the Wind Speed by ANN-PSO
The basic idea of the proposed wind speed estimation is to
retrieve more precision on MPPT mode for any instantaneous
value of the wind speed. It can be noted that the artificial
neural network based particle swarm optimization (ANNPSO) basically behaves as a virtual anemometer, permitting
the free wind speed to be estimated by the inversion of the
wind turbine model. The block diagram of the algorithm is
shown in Fig. 4. The direct model of the wind turbine, given
by (1) – (4), gives the output power of the turbine by means
of an involved nonlinear function of the free wind speed Vw
and the rotor speed ωm. The approximation of the direct
model is not a challenging problem and can be easily carried
out by any neural network (NN) for function approximation
(multilayer perceptron or RBF). However, this is not the case
for the computation of the inverse model of the turbine,
which gives the free wind speed as a function of the machine
speed and power. This is because it is not known a priori if
there exist discontinuities or multiple branches, which makes
conventional NNs unsuitable [3].
According to the direct turbine model, a complete training
set of data has been created, as well as a test set, and then
used to train an ANN with two hidden layers which their
weights are updated through a particle swarm optimization
(PSO).
B. Particle Swarm Optimization (PSO)
PSO is a population-based searching algorithm. PSO
randomly produces npopu particles in searching space, and
each particle includes position X i and velocity Vi, where Xi is
the position of i-th particle in the searching space, Xi=( Xi1,…,
Xij,….,Xik), and Vi is the velocity of i-th particle in the
searching space, Vi=( V i1,…, V ij,….,Vik) [24, 25]. The
position Xi of i-th particle represents a solution of the problem
and the velocity Vi of i-th particle represents its displacement
in the searching space. Pbesti is the optimal position that the
i-th particle has experienced, and pbesti is the optimal fitness
that the i-th particle has experienced. Gbest is the optimal
position that all particles have experienced and gbest is the
optimal fitness that all particles have experienced. When Fit
(.) is the fitness function for solving the maximum value, the
optimal position of each particle is shown in (5).
Pbesti (t+1)=
Pbesti(t)for Fit(Xi (t+1))≤Fit(Pbesti (t))
(5)
Xi (t+1)for Fit(Xi (t+1))>Fit(Pbesti (t))
To improve the convergence, gbest and Gbest are selected
by comparing the experiences of others. Therefore, the i-th
particle is guided to three vectors (Vi, Pbesti, and Gbest). The
inertia weight method, shown as in (6) and (7), is applied to
update velocity and position of the particles [24].
Vnew
ij =w.V ij+c1 .rand1. Pbestij -Xij +c2 .rand2. Gbestij -Xij (6)
Xnew
ij =Xij +V ij (7)
Where
Pbest i=( Pbesti1,…,Pbestij,….,Pbest ik);
Gbest=(Gbest 1,…,Gbestj,….,Gbest k);
w=wmax -iter.(wmax -wmin )/itermax ;
c1 , c2 are acceleration coefficients;
w
is the coefficient of the inertia weight;
iter is the current iteration number.
Given the PSO method described above, the process of
the PSO is shown as the following steps:
Step 1) Generate equivalent npopu quantity of position and
velocity randomly, and record Pbesti, pbesti, gbest,
and Gbest.
Step 2) Calculate each fitness value of particles.
Step 3) If stopping criterion is satisfied (e.g., maximum
iteration number), the procedure would go to the
end; otherwise, proceed to step (4).
Step 4) Update the Pbesti and pbesti.
Step 5) Update the gbest and Gbest.
Step 6) Update particles position and velocity by applying
steps (6) and (7), and then go back to step (2).
IV.
MPPT CONTROL BY DIRECT ADAPTIVE F UZZY-PI
CONTROLLER
A direct adaptive fuzzy-PI controller is designed in order
to track λopt on MPPT mode for a wide range of wind speeds
in the presence of noises and disturbances.
Suppose that D (duty cycle of the boost converter) is the
output of an adaptive fuzzy system in the normalized form
with the inputs and . Three fuzzy membership functions
are considered for each fuzzy input, hence the whole control
space will be covered by nine fuzzy rules. The linguistic
fuzzy rules are proposed in the Mamdani type of the form
FRl:
ℎ
(8)
where FRl denotes the l-th fuzzy rule for l=1,…, 9. In the l-th
rule, , , and are fuzzy membership functions belonging
to the fuzzy variables
,
and D, respectively. Three
( ), named as Positive
Gaussian membership functions,
(P), Zero (Z), and Negative (N) are defined for input in the
operating range of manipulator as shown in Fig. 5. Three
Gaussian membership functions,
( ), named as P, Z, and
N in the same shape as illustrated in Fig. 5, are used for input
. Nine symmetric Gaussian membership functions,
( ),
named as Very Positive High (VPH), Positive High (PH),
Positive Medium (PM), Positive Small (PS), Zero (Z),
Negative Small (NS), Negative Medium (NM), Negative
High (NH), and Very Negative High (VNH) are defined for D
( ) = exp(−(( − )/ ) ) for l= 1,…,9
in the form of
in the operating range of output. The symmetric Gaussian
function depends on two parameters and . In this work,
is adjusted by an adaptive law, whereas is considered as a
fixed scalar.
The fuzzy rules should be defined such that the tracking
control system goes to λopt. An expert’s knowledge, the trial
and error method, or an optimization algorithm such as PSO
may be used to design the fuzzy controller. The obtained
fuzzy rules are given in TABLE I. In this paper, the centers of
Gaussian membership functions for D are adapted to optimize
the performance of the control system.
If the product inference engine, singleton fuzzifier, center
average defuzzifier, and Gaussian membership functions are
used, the fuzzy system is as the following:
( ,
∑
)=
(
∑
)
(
(
)
)
(
)
(9)
( ) ∈ [0,1] and
( ) ∈ [0,1] are the
where
membership functions for the fuzzy sets
and
,
respectively, and is the center of fuzzy set . An important
contribution of fuzzy systems theory is to provide a
systematic procedure for transforming a set of linguistic rules
into a nonlinear mapping as stated in (9). One can easily
manipulate this transformation by regulating from (9) such
that
( | )=∑
where
=
= [ … ] and
(
=∑
= 0.5(
)
(
)
…
)
(
+
∫ ) +
(
∗
−
∗
)(
where is a positive scalar. We differentiate
to time to get
̇ = +
∫
̇+
− (
− ) (17)
with respect
∗
−
) ̇
(18)
From (16) we have
= −
∗
∫ +
−
(19)
Substituting (19) into (18) yields
̇ =
∗
−
+
−
1
̇
(10)
+ is a positive value expressed as
(
=[
For regulating
, we use (16) to suggest a positive
definite function of the form in (17),
,
(11)
)
]
(12)
+
̇−
(
∫
∫ )
(20)
̇ in (20) includes two terms. Therefore, we can control ̇
by regulating which is in the first term of ̇ . This leads to
propose an adaptive law which should be evaluated afterward
as follows:
∗
−
+
−
∫
̇ =0
(21)
Therefore, the law of adaption is obtained by
̇= which
+
∫
is given by
=
Figure 5. Membership functions of the input
(22)
(23)
In order to evaluate the adaptive law (22), we substitute
(21) into (20) to obtain
TABLE I. FUZZY RULES
̇ = +
̇−
(
∫
∫ )
(24)
P
Z
N
N
Z
P
Taking the derivative of
gives
in (19) with respect to time
Z
NS
VNH
PM
Z
NM
VPH
PS
Z
̇ =
−
Using the input scaling factors
and , we have
and
Where
to scale
=
,
(13)
=
̇
(14)
is
+
∗
∫ = (
− )
(15)
+
∫ = (
∗
−
)
(16)
)
(26)
Substituting (25) into (24), to satisfy ̇ < 0 in (24), it is
required that
+
∫
<
+
∫
(27)
According to the Cauchy-Schwartz inequality, it is clear
that:
By substituting (10) into (15),
( ∗
=
∗
Let
in (15) be the ideal control. Hence, the closedloop dynamics of the fuzzy control system can be written as:
(25)
+
Suppose that
∫
≤ +
∫ . | |.
(28)
| |<
TABLE II. WIND-TURBINE PARAMETERS
(29)
where
is a positive scalar. Thus, to satisfy inequality
(27), it is sufficient that
R [m]
2.5
3
ρ [kg/m ]
1.225
λopt
8.1
cannot reduce further to be
∫
. > + ∫ . Considering (30), it verifies that the
minimum value of error will be small if we use a large gain
value . The tracking error is affected by the upper bound of
Cpmax
0.48
Gear box ratio
5
Pole-pairs of PMSG
4
Generator rated power [w]
2827.43
as stated by (30).In summary, the simplified direct adaptive
fuzzy control system is shown in Fig. 6.
Generator rated speed [rpm]
4500
Rated wind speed [m/s]
7.56
.
Note that < +
∫
(30)
+
V. SIMULATION RESULTS
The simulations have been carried out using
MATLAB/Simulink software. The parameters of the wind
generator system are summarized in TABLE II.
Fig. 10 shows Cp during the transient time, which
confirms the results of Fig. 9. Indeed, PI controller cannot
follow Cpmax with zero steady state error.
Wind Speed (m/s)
10
5
Real
Estimated
0
1
2
3
4
5
6
7
time (s)
Figure 7. Real and estimated wind speeds
7.8
7.6
7.4
Wind Speed (m/s)
Fig. 7 shows the real (measured) wind-speed profile as
well as estimation by the ANN-PSO. It can be observed that
the ANN-PSO properly estimates the wind speed both in
steady state and in transients, with negligible estimation
errors. Moreover, for evaluating the robustness of the
adaptive fuzzy-PI controller compared with the conventional
PI controller which is tuned for nonlinear plant at the nominal
operating, a sudden wind change is being applied according
to Fig. 8. Fig. 9 depicts the error of tracking λopt for each
controller. Although PI controller has fewer oscillations for
the rated wind speed before step change at 3 s in comparison
with the proposed method, but it can be observed that a step
change in the wind speed causes a steady state error for
classic PI controller. In contrast the proposed method can
track λopt in about 0.05 s during the MPPT process.
15
7.2
7
6.8
6.6
6.4
0
1
2
3
4
5
time (s)
Figure 8. A step change in wind speed
4
3
Tracking Error
2
1
0
-1
-2
Proposed controller
PI controller
-3
-4
1
1.5
2
2.5
3
3.5
4
4.5
5
time (s)
Figure 6. The direct adaptive fuzzy-PI control system
Figure 9. Error tracking of proposed method and PI controller
5.5
0.48
Coefficient of Power (Cp)
0.46
[12]
0.44
0.42
Proposed controller
0.4
[13]
PI controller
0.38
0.36
[14]
0.34
0.32
0.3
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
time (s)
[15]
Figure 10. The Power coefficient
VI.
CONCLUSION
This paper proposes a robust direct adaptive fuzzy-PI
control for MPPT control. To track the maximum power
point over a wide speed range based on tip speed ratio
control, the information of the wind speed is required. Hence,
we have used an ANN–PSO to estimate the wind tangential
speed. In addition, the authors analysed a simulation on a
PMSG wind turbine using rectifier and a boost converter. By
controlling the duty cycle of the converter, the apparent load
developed by the generator can be adjusted, and thus, its shaft
speed can be tuned. The proposed method obtains the
maximum average value of Cp and maintains it at its
maximum even with changes in wind speed. The simulation
results show the effectiveness of the proposed method.
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