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processes
Article
Integral Sliding Mode Control for Maximum Power Point
Tracking in DFIG Based Floating Offshore Wind Turbine and
Power to Gas
Lin Pan 1,2,3,4 , Ze Zhu 1,*,† , Yong Xiong 5,*,† and Jingkai Shao 6, *,†
Citation: Pan, L.; Zhu, Z.; Xiong, Y.;
Shao, J. Integral Sliding Mode Control
for Maximum Power Point Tracking
in DFIG Based Floating Offshore
Wind Turbine and Power to Gas.
Processes 2021,9, 1016. https://
doi.org/10.3390/pr9061016
Academic Editor: Krzysztof
Rogowski
Received: 13 May 2021
Accepted: 4 June 2021
Published: 9 June 2021
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Attribution (CC BY) license (https://
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4.0/).
1School of Logistics Engineering, Wuhan University of Technology, Wuhan 430063, China;
lin.pan@whut.edu.cn
2Shaoxing Institute of Advanced Research, Wuhan University of Technology, Shaoxing 312300, China
3Zhongshan Institute of Advanced Engineering Technology of WUT, Zhongshan 528437, China
4Key Laboratory of Marine Power Engineering and Technology (Ministry of Transport),
Wuhan University of Technology, Wuhan 430063, China
5School of Navigation, Wuhan University of Technology, Wuhan 430063, China
6Guangxi LiuGong Machinery Co., Ltd., Liuzhou 545007, China
*Correspondence: zhuze1202@whut.edu.cn (Z.Z.); xiong@whut.edu.cn (Y.X.); jingkaishao@hotmail.com (J.S.)
† These authors contributed equally to this work.
Abstract:
This paper proposes a current decoupling controller for a Doubly-fed Induction Generator
(DFIG) based on floating offshore wind turbine and power to gas. The proposed controller realizes
Maximum Power Point Tracking (MPPT) through integral sliding mode compensation. By using the
internal model control strategy, an open-loop controller is designed to ensure that the system has
good dynamic performance. Furthermore, using the integral Sliding Mode Control (SMC) strategy,
a compensator is designed to eliminate the parameter perturbation and external disturbance of
the open-loop control. The parameters of the designed controller are designed through Grey Wolf
Optimization (GWO). Simulation results show that the proposed control strategy has better response
speed and smaller steady-state error than the traditional control strategy. This research is expected to
be applied to the field of hydrogen production by floating offshore wind power.
Keywords:
floating offshore wind turbine; doubly-fed induction generator (DFIG); integral sliding
mode control (ISMC); maximum power point tracking (MPPT); power to gas
1. Introduction
Since the industrial revolution, energy has become the fundamental power for hu-
man production and development. On the one hand, natural reserves of non-renewable
resources such as oil and coal are limited. After being consumed by humans for centuries,
such resources are gradually depleted. On the other hand, after the combustion of various
fossil fuels, a large amount of toxic gas (including nitrogen oxides and sulfur oxides) and
particulate matter will be emitted, which will increase the risk of respiratory diseases [
1
].
Under such circumstances, various renewable energy utilization schemes such as wind
energy and solar energy have been proposed [
2
]. Due to its unique advantages, Doubly-fed
Induction Generators (DFIG) occupy a large proportion in the field of wind power gen-
eration. The performance of the drive control system is directly related to the operating
performance of the generator [
3
]. Therefore, the generator control strategy is the key to
affecting generator performance.
Including doubly-fed induction generators, the induction motors are multi-variable
and strongly coupled systems. The vector control is the strategy, which transforms the
three-phase asynchronous motor system into the DC motor system through coordinate
transformation, thereby achieving independent control of torque and flux components [
4
].
The vector control will overlap the coordinate system with a certain vector of the motor.
Processes 2021,9, 1016. https://doi.org/10.3390/pr9061016 https://www.mdpi.com/journal/processes
Processes 2021,9, 1016 2 of 23
They are the available vectors, such as stator flux, stator voltage, air gap flux, rotor flux,
etc. [
5
]. Generally, a DFIG wind power system using vector control is designed as a double
closed loop structure. The two PI controllers are used to control the speed and reactive
power separately in the outer loop. At the same time, the two PI controllers are used to
control the
d
-axis current component and the
q
-axis current component, respectively, in
the inner loop [
6
]. In [
7
], the author proposed a robust proportional-integral (PI) controller
with its parameters designed by constrained population extremal optimization for the
load frequency control problem. Zeng proposed a hybrid method combined adaptive
control, neural network, and PID and proved its effectiveness for a nonlinear system in [
8
].
For this control structure, some studies have adjusted the parameters of the PI controller
by applying a heuristic algorithm to obtain better power capture performance [
9
,
10
]. Qi
investigated the event-triggered
L∞
control for network-based switched linear systems
with transmission delay in [
11
] and proposed
H∞
filtering for networked switched systems
in [12].
With the development of floating offshore wind turbines over the world, their reliabil-
ity and dynamic performance requirements have gradually increased [
13
,
14
]. Although
vector control theory can be used to convert a doubly-fed floating offshore wind turbine
system into a linear system. However, in fact, the doubly-fed wind turbine system is still
nonlinear, and it often contains a large amount of time delay and coupling components in
the actual working environment [
15
–
17
]. With the increase of coupling effect, its torque may
produce transient distortion, which affects the dynamic performance of the system, and
then causes the maximum power point to not coincide with the actual working
state [18]
.
Therefore, it has been difficult for the simple PI control system to meet the increasingly
high work requirements, and more advanced controllers need to be designed according
to modern control technology. It is worth mentioning that floating offshore wind energy
develops rapidly in developing countries in recent years, such as China.
Floating offshore wind power generation technology provides new ideas for solving
the problem of wind curtailment. It is of great significance for solving the problem of
floating offshore wind power consumption, and development of decentralized wind power
generation technology, realizing multi-channel and efficient use of renewable energy [
19
].
Wind power generation hydrogen is the method by using electrolysis of water energy
storage. On the one hand, it can integrate hydrogen as a clean and high-energy fuel into
the existing gas supply network and realize the complementary conversion of electricity to
gas. On the other hand, it can directly use hydrogen energy in high-efficiency and clean
technologies such as fuel cells. For example, Figure 1shows the description of floating
offshore wind turbines and power to gas [
20
]. Usually, the floating offshore wind turbines
are located in the deep sea and have the advantages of abundant wind resources.
Sliding mode control is a nonlinear control method, which is characterized by discon-
tinuous control. It can make the system switch from one continuous structure to another
continuous structure in the state space, so this is a variable structure control method. The
control design of sliding mode control will change the dynamic characteristics of the sys-
tem so that the state trajectory moves along the boundary of the control structure. This
boundary is called the sliding surface. The sliding surface can be designed as required,
and the movement of the system trajectory on the sliding surface is not affected by the
parameters of the controlled object and external interference. Therefore, sliding mode
control has the advantages of fast response and insensitivity to external interference [21].
In recent years, with the development of computer technology and high-power elec-
tronic switching elements, the realization of sliding mode control has become easier. For
such complex nonlinear systems as wind power systems, it is suitable to use sliding mode
control theory to design controllers that meet performance requirements. It can improve
the dynamic performance of wind turbines by using the sliding mode controller instead of
the PI controller for speed control [
22
,
23
]. In Ref. [
24
], SMC is used for direct power control
of a doubly-fed induction generator wind turbine operating in unbalanced grid voltage
conditions. In Ref. [
25
], an improved strategy of SMC is used for the controller design of
Processes 2021,9, 1016 3 of 23
a variable speed wind turbine with a fractional order doubly fed induction generator. In
Ref. [
26
], a combination of sliding mode control and phase-locked loop estimator is used for
the sensorless vector control strategy of a rotor-tied doubly fed induction generator system.
In Ref. [
27
], an adaptive gain second-order sliding mode direct power control strategy
is proposed, which can work normally in a DFIG wind turbine system with unbalanced
grid voltage.
Figure 1. The description of floating offshore wind turbines and power to gas.
In view of the rich characteristics of floating offshore wind energy resources, this
study focuses on high-power floating offshore wind power generation systems. Based on
the above studies, in order to solve the problem of insufficient dynamic performance and
robustness of traditional dual closed-loop PI controllers, this paper proposes a new MPPT
control strategy. According to the principle of internal model control, an internal model
open-loop controller is designed. In addition, in order to improve the controller’s ability to
resist external disturbances, the sliding mode theory is used to compensate the errors of the
internal-mode open-loop controller. The novelty of this study is the use of a new sliding
mode controller structure. In the proposed control method, a sliding mode controller is
used to compensate the output error instead of directly outputting the control signal. This
is different from most DFIG wind turbine systems based on sliding mode control. In order
to verify the accuracy and reliability of the proposed controller, the proposed controller
was simulated and verified in Matlab software.
The structure of the article is as follows: Section 2describes the DFIG floating offshore
wind turbine system model. Section 3introduces the design of the proposed controller
and gives a detailed proof of system stability. In Section 4, the proposed control method is
simulated, and the simulation results are analyzed. Finally, it is summarized in Section 5.
Processes 2021,9, 1016 4 of 23
2. DFIG Floating Offshore Wind Turbine System Modeling
The doubly-fed floating offshore wind turbine system is shown in Figure 2. The
generator used in this power generation system is a Doubly-Fed Induction Generator [
28
].
The floating offshore wind turbine is connected to the generator rotor through a gearbox.
At the same time, the rotor is excited by a power converter, and the generator stator is
connected to the grid. A variable-speed constant-frequency power generation system using
a doubly-fed floating offshore wind turbine is one of the popular forms of current wind
energy conversion systems. Decoupling control of active and reactive power in floating
offshore wind turbine systems can be achieved by applying dual PWM converters. This
kind of wind energy conversion system has the regulation capability similar to that of
a synchronous motor, and can regulate the voltage and frequency of the power grid. In
addition, the power converter is located on the rotor side, and the power of the rotor side
circuit depends on the generator slip power. Therefore, its actual power is only about 30%
of the generator capacity, which greatly reduces the size and cost of the power converter.
Due to such advantages of the doubly-fed floating offshore wind turbine system, the
industry has conducted in-depth research on the converter control strategy of this system.
Figure 2. Description of the DFIG wind power system.
2.1. Floating Offshore Wind Turbine Model
In the doubly-fed floating offshore wind turbine system, the floating offshore wind
turbine is used to convert wind energy into mechanical energy, and the generator is used
to convert mechanical energy into electrical energy. The mechanical energy is transmitted
between the floating offshore wind turbine and the generator through a transmission
structure such as a transmission shaft and a gearbox. The total amount of mechanical
energy output by a floating offshore wind turbine is mainly determined by the wind speed
and the aerodynamic characteristics of the floating offshore wind turbine. At the same time,
the mechanical energy characteristics delivered to the generator are also closely related to
the mechanical characteristics of the transmission system. The wind energy captured by an
floating offshore wind turbine is usually described by Equation (1) [29]:
Pm=0.5Cp(λ,β)ρAv3(1)
where
Pm
is the output power of the floating offshore wind turbine,
Cp
is the power
coefficient, and it is related to the tip speed ratio
λ
and pitch angle
β
,
ρ
is the air density,
A
is the area swept by the pales of the turbine, and vis the wind speed.
The power coefficient can be written as Equation (2) [30]:
Cp(λ,β)=c1c2
λi
−c3β−c4e−c5
λi+c6λ
1
λi
=1
λ+0.08β−0.035
β3+1
(2)
The definition of tip-speed-ratio
λ
is as the follows. The ratio of the linear velocity of
the floating offshore wind turbine blade tip to the wind speed is
λ
, that is,
λ=ωR/v
,
Processes 2021,9, 1016 5 of 23
ω
is the angular speed of the floating offshore wind turbine,
R
is the blade length, and
ci(i=
1, 2, 3, 4, 5, 6
)
are constants related to the characteristics of the floating offshore wind
turbine. The parameters used in this study are
c1
= 0.22,
c2
= 116,
c3
= 0.4,
c4
= 5,
c5
= 12.5,
and c6= 0.
The relationship between power coefficient, tip speed ratio, and pitch angle is shown
in Figure 3.
12345678
0
0.1
0.2
0.3
0.4
0.5
0.6
Cp
= 0
= 5
= 10
= 15
Figure 3. Aerodynamic characteristics of floating offshore wind turbines.
It can be known from the above analysis that there is an optimal tip speed ratio
λopt
,
which makes the captured wind energy the largest by the floating offshore wind turbine at
this tip speed ratio. Therefore, the reference value of the rotational speed of the floating
offshore wind turbine can be given by Equation (3):
ω∗
r=λoptv/R(3)
2.2. DFIG Model
The mathematical model of an induction motor has the characteristics of multi-
variable, strong coupling, nonlinearity, and time-varying. It is very inconvenient to analyze
it. The original model can be transformed by vector control theory to obtain the state equa-
tion of DFIG in the synchronous rotating coordinate system [
28
]. Its dynamic characteristics
can be described by Equations (4) and (5):
usd
usq
urd
urq
=
Rs0 0 0
0Rs0 0
0 0 Rr0
0 0 0 Rr
isd
isq
ird
irq
+
p−ω10 0
ω1p0 0
0 0 pωr−ω1
0 0 ω1−ωrp
ψsd
ψsq
ψrd
ψrq
(4)
Processes 2021,9, 1016 6 of 23
Te=3
2np(ψsdisq −ψsqisd) = TL+J
np
dωr
dt +D
np
ωr(5)
where
usd
and
usq
are voltage components of the stator in
d
-axis and
q
-axis,
urd
and
urq
are
voltage components of the rotor in
d
-axis and
q
-axis,
isd
and
isq
are current components
of the stator in
d
-axis and
q
-axis,
ird
and
irq
are current components of the rotor in
d
-axis
and
q
-axis,
Rs
and
Rr
are the resistances of the stator and rotor,
ψsd
and
ψsq
are the flux
components of the stator in
d
-axis and
q
-axis, and
ψrd
and
ψrq
are the flux components
of the rotor in
d
-axis and
q
-axis.
ω1
is the synchronous electromagnetic angular velocity,
ωr
is the rotor electromagnetic angular velocity,
p
is the differential operator,
Te
is the
electromagnetic torque,
np
is the number of pole pairs,
TL
is the external load,
J
is the
moment of inertia, and Dis the damping coefficient.
The relationship between flux and current is shown in Equation (6):
ψsd
ψsq
ψrd
ψrq
=
Ls0Lm0
0Ls0Lm
Lm0Lr0
0Lm0Lr
isd
isq
ird
irq
(6)
where
Ls
is the stator inductance,
Lr
is the rotor inductance, and
Lm
is the
mutual inductance.
In stator flux orientation vector control, the direction of the stator flux is coincident
with the
d
-axis of the synchronous rotation coordinate system. Assuming that the DFIG
winding is directly connected to an infinitely large power grid, parameters such as the
voltage amplitude, phase, and angular frequency of the grid can be considered as the
constant, and the stator flux can be regarded as a fixed value. If the stator resistance is
ignored, ψsd =ψsand ψsq =0. One has the following results in Equations (7) and (8):
(usd =pψs=0
usq =ω1ψs=us
(7)
isd =ψs
Ls
−ird Lm
Ls
isq =−irq Lm
Ls
(8)
Substituting Equations (7) and (8) into (4), we know that
dird
dt =−Rr
σLr
ird + (ω1−ωr)irq +1
σLr
urd
dirq
dt =−Rr
σLr
irq −(ω1−ωr)( Lm
σLsLr
ψs+ird) + 1
σLr
urq
(9)
where σis the leakage coefficient, and its definition is shown in Equation (10):
σ=1−L2
m
LsLr
(10)
It can be known from the above analysis that the decoupling of active power and reactive
power of the stator has been realized by vector control. Generator stator active power can be
controlled by the rotor current
q
-axis component, and stator reactive power can be controlled
by the rotor current
d
-axis component. Considering that the rotor voltage balance is not
completely decoupled, the feedforward term is defined as shown in Equation (11):
urd0= (ω1−ωr)σLrirq
urq0=−(ω1−ωr)( Lm
Ls
ψs+σLrird)(11)
Processes 2021,9, 1016 7 of 23
where
urd0
and
urq0
are voltage feedforward components of the rotor in
d
-axis and
q
-axis.
The
d
-axis and
q
-axis current component can be decoupled, and the entire system can be
regarded as a first-order inertial system. The transfer function of the system is shown in
Equation (12):
ird(s)
irq(s)=G(s)urd0(s)
urq0(s)
="1
Rr+sσLr0
01
Rr+sσLr#urd0(s)
urq0(s)(12)
where
urd0
and
urq0
are voltage components of the rotor in
d
-axis and
q
-axis after decoupling.
Equation
(12)
shows that, if the grid voltage is constant, the electromagnetic torque of DFIG
is proportional to the current component of the rotor in
q
-axis, that is, the electromagnetic
torque can be controlled by the rotor q-axis current.
In summary, the DFIG equivalent model under stator flux orientation vector control
is shown in Figure 4. By controlling the
q
-axis component of the rotor current, the active
power of the DFIG can be controlled. By controlling the
d
-axis component of the rotor
current, the DFIG reactive power can be controlled. Therefore, controlling the
d
-axis and
q
-axis components of the DFIG rotor current can control the output power of the generator.
Since the electromagnetic torque can also be controlled by the rotor current, the DFIG speed
control can be further realized.
Figure 4. DFIG-model under stator flux orientation vector control.
3. Current Decoupling Based on Integral Sliding Mode Control
3.1. Internal Model Controller
Internal model control is based on the process mathematical model for the controller
design. It was proposed and applied to wind turbine in 2018 [
31
]. This control method has
a good effect on solving tracking problems and anti-jamming problems, and it also has
robustness to model uncertainty problems. Its basic control structure is shown in Figure 5.
In Figure 5, where
G(s)
is the system model transfer function,
M(s)
is the internal
model transfer function,
C(s)
is the controller transfer function,
F(s)
is the internal model
control transfer function,
R(s)
is the reference input signal,
E(s)
is the error signal,
U(s)
is the control system output signal,
D(s)
is the interference signal, and
Y(s)
is the system
output signal.
Processes 2021,9, 1016 8 of 23
Figure 5. Description of internal model control.
According to Figure 5, the system input–output transfer function is shown in Equa-
tion (13).
Y(s) = C(s)G(s)
1+Cs[Gs −Ms]R(s) + 1−C(s)G(s)
1+Cs[Gs −Ms]D(s)(13)
It is assumed that the internal model can be fully described by the system model, that
is,
M(s) = G(s)
. When
C(s) = M−1(s)
, there is
Y(s) = R(s)
. In this ideal state, it is not
necessary to adjust any control parameters to make the output of the system fully track the
reference input. In addition, since the system output does not include interference signal
components, the controller can be considered to be able to overcome any
interference signals.
However, in an actual system, the above ideal controller is difficult to implement for
the following reasons:
(i)
When the controlled system
G(s)
contains time-delay components, the controller
C(s)
will contain lead components, which does not conform to physical reality and is
difficult to achieve;
(ii) When the right half-plane zeros exist in the controlled system
G(s)
, the controller
C(s)
will contain the right half-plane poles, and the controller will be unstable at this time,
which will affect the stability of the entire system;
(iii)
When the order of the denominator polynomial in the controlled system
G(s)
is
higher than the numerator, the controller
C(s)
will include a differentiator. Since the
differentiator is extremely sensitive to signal noise, it is not suitable for practical use;
(iv)
When there is a model error, that is,
M(s)6=G(s)
, the ideal controller will not
guarantee the stability of the system.
Due to the above reasons, there are two steps in the designing of the controller. First,
the controlled system
G(s)
is been decomposed. The smallest phase part has been found
that does not include the time delay components and the zero point in the right half
plane. The minimum phase part is the internal mode
M(s)
of the control system. Then,
the controller is constructed by inverting the internal model and adding a filter, which is
shown in Equation (14):
C(s) = L(s)
M(s)(14)
where L(s)is a low-pass filter, as shown in Equation (15):
L(s) = α
(s+α)(15)
where αis a modulation coefficient.
Combined with Equation
(12)
, the internal model controller can be obtained as shown
in formula (16):
F(s) = α(Rr
s+σLr)(16)
Processes 2021,9, 1016 9 of 23
The controller proposed according to the internal model theory is not difficult from
the PI controller in form, but the internal model controller has only one parameter that
needs to be adjusted.
If the internal model parameters are completely consistent with the actual system
parameters, the actual input signal can be replaced by the internal model’s response to the
output signal. Giving the definition of the system output estimate
ˆ
Y(s)
, which is shown in
Equations (17) and (18):
ˆ
Y(s)=ˆ
ird(s)
ˆ
irq(s)=1
Rr+sσLrurd0(s)
urq0(s)(17)
ˆ
ur0=ˆ
urd0
ˆ
urq0="−(ω1−ωr)σLrˆ
irq
(ω1−ωr)( Lm
Lsψs+σLrˆ
ird)#(18)
An open-loop internal model controller is obtained, which is shown in Figure 6.
Figure 6. Description of the internal model open-loop controller.
3.2. Integral Sliding Mode Compensation
Due to external disturbances in the actual system, the model parameters may not
be accurate enough. The estimated current of the open-loop controller will deviate from
the actual current. Therefore, in order to improve the robustness of the control system,
a sliding mode control strategy is introduced. The tracking error function is defined as
shown in Equation (19):
e=ˆ
ird
ˆ
irq +z
˙
z=Rr
σLrird
irq −1
σLrurd −ˆ
urd0
urq −ˆ
urq0
z(0) = [0 0]T
(19)
Processes 2021,9, 1016 10 of 23
The open-loop controller is designed based on the internal model control theory. It can
achieve good performance when the system reaches the equilibrium position, but when
the system state is unbalanced at the initial moment and there is external interference, the
internal-mode open-loop controller cannot obtain good control performance. For such
applications, the integral sliding mode theory can be introduced to design the integral
sliding mode surface. According to the integral sliding mode theory, the sliding mode
surface is usually defined according to Equation (20):
S(t)=δ+d
dt r−1
e(t)+kiZ∞
0e(t)dt (20)
where
r
is the system order,
δ
is a positive real number, and
ki
is a sliding gain. It can be
known from Equation (18) that r=1 and δ=1.
Integral sliding mode control adds an integral part to the basic sliding mode control
method to improve the performance of sliding mode control. Sliding mode control is robust
to disturbances only in the sliding mode phase, but it is not robust in the arrival phase.
Since the integral sliding mode control includes an integral part, a sliding surface can be
designed so that the system is in the sliding mode phase at the initial moment. Thus, the
entire state trajectory of the system is on the sliding surface [
32
]. The designed sliding
surface is shown in Equation (21):
S(t) = e(t) + kiZ∞
0e(t)dt (21)
The current estimate satisfies Equation (22):
d
dt ˆ
ird(t)
ˆ
irq(t)=1
σLrurd0(t)
urq0(t)−Rr
σLrˆ
ird(t)
ˆ
irq(t)(22)
Substituting Equation
(22)
into Equation
(9)
, the derivative of the sliding mode surface
is shown in Equation (23):
˙
S=1
σLrurd0+ˆ
urd0−urd
urq0+ˆ
urq0−urq +Rr
σLrird −ˆ
ird
irq −ˆ
irq +kie(23)
The stability of sliding mode control can usually be judged by Lyapunov function, as
shown in Equation (24):
V=1
2S2(24)
In order to ensure that Lyapunov function is negative definite, that is,
˙
V≤
0, the
control law is designed as shown in Equation (25):
urd
urq =urd0+ˆ
urd0
urq0+ˆ
urq0+Rrird −ˆ
ird
irq −ˆ
irq +σLr[kie+εsign(S)] (25)
Substituting the above Equation
(25)
into the Lyapunov function Equation (24),
Equation (26)
can be obtained:
˙
V=ST(−esign(S)) (26)
Therefore, as long as the constant e>0 is satisfied, ˙
V≤0 can be ensured.
Considering the impact of uncertainties and disturbances on the system, the sliding
mode surface can be rewritten into the form of Equation (27):
˙
S=1
σLrurd0+ˆ
urd0−urd
urq0+ˆ
urq0−urq +Rr
σLrird −ˆ
ird
irq −ˆ
irq +kie+τd(27)
Processes 2021,9, 1016 11 of 23
where
τd
is the influence of the uncertainties and disturbances on the sliding surface.
Equation (26) can be rewritten as:
˙
V=ST(−esign(S) + τd)(28)
As long as
e>|τd|
is satisfied,
˙
V≤
0 can be ensured. This shows that the proposed
control method can ensure stability under disturbances.
Remark 1.
According to the characteristics of sliding mode control, the state trajectory of the system
will be limited to the sliding surface after the system state moves to the sliding surface. However,
in practical systems, due to the inertia of the controlled system and the delay of the switching
components, the switching frequency of sliding mode control cannot be infinite. This will cause the
trajectory of the system state to not stay on the sliding surface, but to traverse back and forth on
the boundary of the sliding surface or to perform periodic motion near the equilibrium point. This
high-frequency oscillation phenomenon is called chattering. Chattering affects the control accuracy
of the system and cause frequent switching of switching components, shortening the component
operation cycle and increasing power consumption.
Remark 2.
For floating offshore wind turbine systems, if chattering occurs in the DFIG drive
control system, it may cause speed fluctuations, torque ripples, and current harmonics. If chattering
occurs in the voltage or flux observer, it will cause observation noise and reduce system stability.
Although sliding mode control has the advantage of good robustness, to some extent, chattering
phenomenon hinders its control advantage. Therefore, the suppression of chattering has become the
primary issue in practical application research of sliding mode control.
In the sliding mode control system of this study, due to the introduction of integral
sliding mode control, the initial state of the system can be located on the sliding surface.
Therefore, the design of the approach law should mainly be considered as the suppression
of chattering. Based on the above analysis, the control law is shown by Equation (29):
˙
S(t)=−k
D(S(t))tanh(γS(t))
D(S)=e+ (1−e)e−η|S|
(29)
where 0
<e<
1,
η>
0, and
γ>
0,
tanh(S)
is a hyperbolic tangent function, and its
expression is shown in Equation (30):
tanh (S)=eS−e−S
eS+e−S(30)
The relationship between the sliding function and its derivative under different pa-
rameter values is shown in Figure 7.
It can be known from Figure 7that the approaching speed of the system is related to
the current value of the sliding function. The larger the value of the sliding function, the
faster the approaching speed. When the state of the system is close to the sliding surface,
that is, the sliding function approaches 0, and the properties of the law of approximation
approximate the hyperbolic tangent function. At this time, the characteristics of the system
are basically determined by parameter
γ
. The hyperbolic tangent function is a continuous
odd function. When it is far from the zero point on the positive semi-axis, its function
value is approximately 1. When it is close to the zero point, its function value will rapidly
decrease to 0. This characteristic allows the approach law to retain the robustness of the
sliding mode control while suppressing chattering. When the parameter
e
is close to 1,
the characteristic of the law of approximation over the entire state space is similar to the
hyperbolic tangent function. That is, when the system state is far from the sliding surface,
the approaching speed is approximately constant. When the system state is close to the
Processes 2021,9, 1016 12 of 23
sliding surface, the approaching speed is rapidly reduced to 0. When the parameter
e
is close to 0, the approaching speed farther from the sliding surface approximates an
exponential relationship with the value of the sliding function. Therefore, the value of
e
affects the characteristics of the approaching law when it is far away from the sliding
surface, that is, the reaching phase of sliding mode control. The parameter
η
affects the
transition process of the two characteristics of the system state when it is far away from
and close to the sliding surface. When the value of this parameter is larger, the approach
speed will converge closer to the sliding surface.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
S
0
0.5
1
1.5
2
2.5
|dS/dt|
=0.7, =2, =10
=0.5, =2, =10
=0.7, =10, =10
=0.7, =2, =100
Figure 7. Reaching law under different parameters.
Theorem 1.
According to the analysis in Equations (29) and (30), the control law of the improved
sliding mode controller is shown in Equation (31):
urd
urq =urd0+ˆ
urd0
urq0+ˆ
urq0+Rrird −ˆ
ird
irq −ˆ
irq +σLr[kie+kp
P(S(t))tanh(γS)] (31)
Proof.
To verify the stability of the proposed system, substituting the control law
(31)
into
the Lyapunov function described in Equation (24), we can get
˙
V=−STk
D(S(t)) tanh(γS)(32)
Since 0 <e<1, η>0.
D(S) = ε+ (1−ε)e−η|S|>0 (33)
It can be concluded that
˙
V=−STk
D(S(t))tanh(γS)≤0 (34)
Processes 2021,9, 1016 13 of 23
The equal sign holds if and only if
S=
0. Therefore, it can be proved that the proposed
sliding mode controller meets the stability requirements.
Taking the current
d
-axis component as an example, the structure of the proposed
internal model-integral sliding model controller(IM-ISMC) is shown in Figure 8. As we
can see in the figure, in the block diagram of the internal model-integral sliding model
controller, an improved approach law has been used on
ui
. Moreover, the tracking error
calculation has been used on error e, and the final output is urd.
Figure 8. Description of block diagram of the IM-ISMC.
In summary, by using the IM-ISMC controller instead of the PI controller in vector
control, an IM-ISMC-based floating offshore wind turbine system can be obtained, as
shown in Figure 9. As we can see in the figure, an IM-ISMC controller has been used at the
back of PI controller. Moreover, the coordinate transformation has been used on PWM and
IGBT, and angle calculation has been used at the back of DFIG.
The proposed control system is based on vector control theory. The relationship
between the
q
-axis component of the rotor current and the speed can be better described
by a linear system, and it can be controlled by a PI controller. The relationship between
the
d
-axis component of the rotor current and the reactive power is similar. The current is
decoupled by the IM-ISMC controller.
The proposed control strategy contains many undetermined parameters, which in-
clude modulation coefficient
α
, sliding gain
ki
, and related parameters of sliding mode
control law
kp
,
e
,
η
, and
γ
. The Grey Wolf Optimization (GWO) will be used to optimize
these parameters.
Grey Wolf Optimization is a meta-heuristic algorithm proposed by Mirjalili of Griffith
University [
33
]. This algorithm is inspired by the hunting behavior and cooperative behav-
ior in the hunting process of gray wolves. The gray wolf family has a strict hierarchical
management system. According to leadership, the wolf group can be divided into four
levels: α,β,δ, and ω.
Processes 2021,9, 1016 14 of 23
Figure 9. Description of floating offshore wind turbine system based on IM-ISMC.
After obtaining the position of the prey, the gray wolves will surround the prey. This
process can be expressed by Equation (35):
(Dp=|C·Xp(k)−X(k)|
X(k+1) = Xp(k)−A·Dp
(35)
Among them,
k
is the number of iterations,
X(k)
is the position vector of the gray
wolf after performing the
k
th iteration,
Xp(k)
is the position vector of the prey after
performing the
k
th iteration,
A
and
C
are coefficient vectors, and the expressions are shown
in Equation (36):
(A=2ar1−a
C=2r2
(36)
Among them,
r1
and
r2
are random numbers in the range of [0,1].
a
is a variable that
linearly decreases with the number of iterations, and its value gradually decreases from 2
to 0.
Through the above iterative process, the individual can be redirected to any position
around the prey. However, this is not enough to reflect the group wisdom in the gray
wolves. When gray wolves are hunting prey, the higher-level gray wolves play a key role in
this process. After the encirclement process is completed, the gray wolves will hunt under
Processes 2021,9, 1016 15 of 23
the leadership of wolves with three levels of
α
,
β
, and
δ
. This process can be described by
the following equations:
Dα=|C1·Xα(k)−X(k)|
Dβ=|C2·Xβ(k)−X(k)|
Dδ=|C3·Xδ(k)−X(k)|
(37)
X1=Xα(k)−A1Dα
X2=Xβ(k)−A2Dβ
X3=Xδ(k)−A3Dδ
(38)
X(k+1) = X1+X2+X3
3(39)
When the process of encirclement and hunting has been completed by the gray wolves,
they will attack the prey. This stage is manifested as the convergence of the solution in the
process of solving the optimization problem.
In the offshore wind power generation system proposed in this paper, a set of pa-
rameters satisfying the definition are regarded as feasible solutions, and all combinations
of parameters satisfying the definition constitute the solution space of the optimization
problem. Using the gray wolf optimization algorithm to search in the solution space, the
sub-optimal solution can be obtained in a limited time.
Usually, the basic method of power to gas from floating floating offshore wind power
is using electrolysis of sea water to produce hydrogen. The principle of electrolyzing water
to produce hydrogen is shown in Figure 10. It can be seen from the figure that the loss of
electrons at the anode produces oxygen, and the electrons at the cathode produce hydrogen.
The solution mixed in water increases the conductivity of the electrolyte. That is to say,
the electrolysis of water is to immerse the cathode and anode in the electrolytic cell in
water and apply direct current, respectively. The water will be decomposed and produce
hydrogen at the cathode and oxygen at the anode. The main chemical reaction equations
of the electrode reaction are as follows:
In the water,
H2O=H++OH−(40)
The point of cathode,
4H++4e+=2H2(41)
The point of anode,
4OH−−4e−=2H2O+O2(42)
The chemical equation for the overall reaction is:
2H2Oelectrolysis
−→ 2H2+O2(43)
The industrial experiment intends is to use a megawatt-class floating offshore wind
turbine and hydrogen production equipment to verify the optimization effect of the control
system. From the perspective of the system, concrete floating foundation, offshore wind tur-
bine, hydrogen production equipment, the theory, method, and algorithm of this research
can be verified step by step. At the same time, during the verification process, the floating
offshore wind power sensing device is used to obtain the real-time status information of the
intelligent control operation energy conversion online, and the controller data acquisition
device is used to obtain the status information related to the wind power operation and the
hydrogen production process. All relevant data are collected and aggregated through the
distributed information network system. The non-grid-connected hydrogen production
and logistics of floating offshore wind power to be used in industrial experiments are
shown in Figure 11.
Processes 2021,9, 1016 16 of 23
Figure 10.
The principle of hydrogen production by water electrolysis of floating offshore
wind power.
Figure 11.
The description of the non-grid-connected hydrogen production and logistics of floating
offshore wind power.
Processes 2021,9, 1016 17 of 23
4. Simulation Results
To verify the effectiveness of the proposed controller, MATLAB/Simulink is used
for simulation verification. The DFIG parameters used in the simulation are shown in
Table 1.
The values of the parameters in the table are selected with reference to real 2 MW
wind turbines.
Table 1. DFIG parameters.
Name Value Unit
Rated power 2000 kW
Stator voltage 690 V
Number of pole pairs (p) 2
Voltage frequency 50 Hz
Stator resistance (Rs) 0.0025 ohm
Rotor resistance (Rr) 0.003 ohm
Mutual inductance (Lm) 2.5 mH
Stator inductance (Ls) 2.51 mH
Rotor inductance (Lr) 2.51 mH
Moment of inertia (J) 120 kg·m2
The effect of the controller is evaluated by testing the response of the control system
at random wind speeds. Considering that the maximum point tracking operation of the
floating offshore wind turbine is between the cut-in wind speed and the rated wind speed,
the wind speeds used in the simulation are in the interval from 3 m/s to 12 m/s. It is
shown in Figure 12.
Figure 12. Wind speed characteristics.
Figure 13 shows the variation curve of the rotor speed under the random wind speed
when the proposed controller and PI controller are used. Figures 14–16 are the rotor speed
in the intervals of 3 s, 7 s, 7 s, 11 s, and 11 s, 15 s, which are obtained by magnifying the
three parts of Figure 13. Due to the mechanical inertia of the generator, there is a certain
delay between the actual speed and the reference speed. Overall, the proposed controller
has better dynamic response speed than the PI controller.
Processes 2021,9, 1016 18 of 23
Figure 13. Simulation results of rotor speed.
3 3.5 4 4.5 5 5.5 6 6.5 7
time(s)
60
80
100
120
140
160
180
rotor speed(rad/s)
reference
IM-ISMC
PI
Figure 14. Rotor speed 3–7 s enlarged view.
Processes 2021,9, 1016 19 of 23
7 7.5 8 8.5 9 9.5 10 10.5 11
time(s)
80
100
120
140
160
180
200
220
rotor speed(rad/s)
reference
IM-ISMC
PI
Figure 15. Rotor speed 7–11 s enlarged view.
11 11.5 12 12.5 13 13.5 14 14.5 15
time(s)
100
120
140
160
180
200
220
rotor speed(rad/s)
reference
IM-ISMC
PI
Figure 16. Rotor speed 11–15 s enlarged view.
Figure 17 shows the corresponding reactive power curves of the two controllers. The
reference value of reactive power is 0 W. The proposed controller can converge faster,
Processes 2021,9, 1016 20 of 23
but the PI controller will oscillate near the equilibrium position. Therefore, the proposed
controller has better steady-state performance than the PI controller.
Figure 17. Simulation results of reactive power.
Figure 18 shows the simulation results of the power coefficient. The maximum power
coefficient is 0.438 approximately. The proposed controller can adjust the rotor speed
according to the change of wind speed, so the power coefficient of IM-ISMC controller is
larger than PI controller in general. The purpose of the maximum power point tracking is to
capture wind energy as much as possible, and the offshore wind energy power coefficient
can be used as the basis for determining the amount of captured offshore wind energy.
This means that floating offshore wind turbine systems can capture more offshore wind
energy by using the proposed controller.
Figure 18. Simulation results of power coefficient.
Processes 2021,9, 1016 21 of 23
Figure 19 shows the different active power between the PI controller and the proposed
controller. They are obtained by subtracting the active power value of the PI controller
from the active power value of the proposed controller. At the beginning of the simulation,
the power differential reaches its maximum value of 90 kW or so. In general, the proposed
controller has higher active power than a PI controller at all times, especially in the time of
the rotor increasing speed.
0 5 10 15
time(s)
-1
0
1
2
3
4
5
6
7
8
9
active power(W)
104
Figure 19. The active power between the PI controller and the proposed controller.
5. Conclusions
A current decoupling controller is presented for DFIG wind power systems on a
floating offshore wind turbine to achieve MPPT. By using the internal model control strat-
egy, an internal model open-loop controller is designed to simplify the parameter design.
Moreover, the sliding mode control theory is used to achieve dynamic compensation based
on the internal model open-loop controller, whereas the integral sliding mode controller
is used to compensate the output error of the open-loop controller, and the parameters
of proposed controller are designed through Gray Wolf Optimization. In addition, the
performance of the controller is verified by testing the response of the controller under
random wind speed in simulation software. Simulation results show that the proposed
controller is superior to traditional PI controllers in terms of dynamic response and steady-
state error. However, the proposed controller is not implemented on real floating offshore
wind turbines. At the same time, how the controller parameters affect the control results
has not been studied in depth. In future research, it is possible to build an experimen-
tal platform to conduct further research on the field of hydrogen production by floating
offshore wind power.
Author Contributions:
L.P.: Conceptualization, Methodology, Software, Data curation, Supervision,
Writing—review & editing, Formal analysis, Resources; Z.Z.: Conceptualization, Visualization, Inves-
tigation, Software, Validation, Funding acquisition, Project administration; Y.X.; Writing—review &
editing, Formal analysis, Resources, Software; J.S.: Visualization, Investigation, Software, Validation,
Writing—original draft. All authors have read and agreed to the published version of the manuscript.
Funding:
This work was supported by the Foundation of Zhongshan Institute of Advanced Engineer-
ing Technology of WUT (Grant No. WUT202001), China. This work was also supported by projects
from Key Lab. of Marine Power Engineering and Tech. authorized by MOT (KLMPET2020-01), the
Processes 2021,9, 1016 22 of 23
Fundamental Research Funds for the General Universities (WUT: 2021III007GX) and Shaoxing City
Program for Talents Introduction, China.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The study did not report any data.
Acknowledgments:
This work was supported by the Foundation of Zhongshan Institute of Advanced
Engineering Technology of WUT (Grant No. WUT202001), China. This work was also supported by
projects from the Key Lab of Marine Power Engineering and Tech authorized by MOT (KLMPET2020-
01), the Fundamental Research Funds for the General Universities (WUT: 2021III007GX), and Shaoxing
City Program for Talents Introduction, China.
Conflicts of Interest: The authors declare no conflict of interest.
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