Oscillations Damping and Maximization of Wind Energy Using A
Fractional Order PID Controller
TAREK A. BOGHDADYa, SAUD N. ALAJMIb, M. A. MOUSTAFA HASSANc, A. A. SEIFd
Department of Electrical Engineering, Faculty of Engineering
Cairo University, Giza, EGYPT
Abstract: - Renewable energy resources are the favorable solution for the coming energy. So, a great interest
has been paid in the last decades for developing and utilizing renewable energy resources such as wind energy.
As it has a large energy content and, particularizes with the availability, the major problems of it is represented
in unmatched with load demand because of the intermittency and fluctuation of natural conditions. Different
optimization methods are presented and discussed like Genetic Algorithm (GA), Grey Wolf Optimization
(GWO). These optimization methods are used to obtain the optimum parameters for Proportional Integral (PI)
controller and the fractional-order PI. The PI and FOPI parameters’ gains are optimized and obtained. For more
clarification for the wind farm performance in the case of using PI controller and fractional-order PI, a three-
phase and single-phase fault are applied to the system. The performance analysis for the system due to these
faults is obtained and discussed.
Key-Words: - Genetic Algorithm, Grey Wolf Optimization, PMSG, Renewable energy, Wind turbine.
Received: March 19, 2021. Revised: January 9, 2022. Accepted: January 24, 2022. Published: February 16, 2022.
1 Introduction
Wind energy is one of the important types of
renewable energy as it is clean, inexhaustible and
has low running cost [1-3].
Damping the oscillations and increasing the
extractable power of wind turbines are challenging
tasks. Wind power plants are extremely complex
systems, and they always rely on automatic control
for satisfactory operation. To operate safely and
efficiently, the need for a robust control is increased
as there are many uncertainties caused by
linearization, noise accompanied with
measurements, and parameters variation with time.
Increasing interest has been directed to develop
wind energy generation. The electrical controller
can achieve a lot of objectives especially in wind
turbines that have variable speeds [4-8].
The PI controller is very common in many industrial
applications as it is reliable, familiar, and easy in
implementation. The challenging task is how to tune
the PI parameters. Using of conventional techniques
were not accurate in tuning the PI parameters.
Ziegler-Nicholas was used depending on loop
testing [9, 10]. While, today the focus is on
intelligent control as Artificial Neural Network
(ANN) controller, Fuzzy Logic Controller (FLC),
and Evolutionary Algorithms (EA) based controller
[11].
There are many evolutionary algorithms such as
Genetic Algorithms (GA) based on natural
selection, Particle Swarm Optimization (PSO) based
on the social behavior of bird flocking and fish
schooling, and Harmony Search (HS) based on
music improvisation process [12-17].
The first method that is being used here is GA. It is
one of the most popular metaheuristic methods
because it is a robust and reliable method; it is based
on Darwin's principles of "the survival of the
fittest". The large fitness according to the
optimization process has the superior probability to
generate a new generation.
The second method that is being used here is Grey
Wolf Optimization (GWO) [18], which is a recently
developed EA in the scientific search.
This paper is organized as follows. A comparison
between the optimization techniques is carried out
in section 2 to select one of them for PI and FOPI
tunning problems. Section 3 presents the electrical
model of the wind power plant, simulation, and
discussion of PMSG in normal and abnormal cases
are presented. Finally, Section 4 summarizes the
simulation results.
2 Testing the Optimization
Techniques
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Improving the controller performance by tracing the
reference signal (i.e. reducing the error between the
measured and reference signals) in an industrial
process is considered an important task by using
PID controller, while finding the optimum
parameters value of PID controller is considered a
very difficult task. Most PID tuning techniques use
conventional methods such as frequency response
which requires considerable technical experience to
apply those formulas. Due to their difficulties, PID
controller parameters are rarely tuned optimally.
The aim here is to test GWO and carry out a
comparison between its performance with PSO, GA,
and Linearized Biogeography-Based Optimization
(LBBO) [19-20]. The squared error integral criteria
is the objective function to be minimized in the step
response of a process which is cascaded with a PID
controller as shown in Figure 1 by tuning the
proportional gain (Kp), integral gain (Ki), and
differential gain (Kd) using MATLAB/SIMULINK.
PID Plant
Input Error
E(s) Controller
output U(s) Output
Fig. 1: Block diagram of the tested systems
Table 1 shows seven transfer functions of
benchmark systems of different orders that will be
used here for testing GWO performance. The tuned
gains obtained by using GWO algorithm are given
in Table 1, while Table 2 presents the tuned gains
that have been obtained using three algorithms.
For the first plant, the values of Kp, Ki, and Kd
founded by GWO, GA, and LBBO are nearly the
same, while the PSO solution is drifted by about
40% of the values found by other algorithms. This is
reflected in the objective function values as shown
in Table 2 where PSO has the worst objective
function value. The results of the three algorithms
(GWO, GA, and LBBO) applied to plants 2, 4, and
6 are nearly the same optimized value. Plant 4, it is
shown that the PSO results in unstable controller
performance, while approximately the same results
(i.e controller response) are obtained using the other
three algorithms. Also, the GWO obtained results
for plants 3, 5, and 7 are much better than the other
algorithms, the GWO has approximately a reduction
from 21% to 45% in the optimized value.
Table 3 indicates that GWO produces better results
with a lower number of objective function
evaluation. The unit step response for the test plants
using the four optimization algorithms PSO, GA,
LBBO, and GWO for tuning the PID parameters are
shown in Figure 2 through Figure 8. In all cases,
GWO has the fastest settling time.
Table 1. The tuned values obtained by GWO
Plant
No.
Transfer function
GWO
Kp
Ki
Kd
1
1.423
0
1.2030
2
30
0
18.985
3
25
0
03045
4
0.319
0.102
0.4333
5
8.423
7.265
0.2017
6
15
1.1761
12.387
7
10
2.500
2.932
Table 2. The tuned values for LBBO, GA, PSO.
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Table 3. Objective functions values obtained by
GWO, LBBO, GA and PSO (the lowest value in
each row is shown in black boldface)
Plant
No.
Best Min. Objective Function
GWO
LBBO
GA
PSO
1
1.102
1.3132
1.9746
1.9520
2
0.9523
0.6497
0.6505
2.2400
3
0.0010
0.0105
0.216
0.1469
4
1.8773
1.9392
2.1500
21.7600
5
0.0212
0.0239
0.3661
0.3697
6
0.8867
0.9078
0.9513
2.5600
7
0.2153
0.2952
0.5374
1.5330
Fig. 2: Plant number 1 output response.
Fig. 3: Plant number 2 output response.
Fig. 4: Plant number 3 output response.
Fig. 5: Plant number 4 output response
Fig. 6: Plant number 5 output response.
Fig. 7: Plant number 6 output response.
Fig. 8: Plant number 7 output response.
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3 System Description and Modeling
A direct-drive PMSG wind turbine is shown in
Figure 9. The PMSG output power is fed to the
utility side through generator side converter with a
DC link than a grid side converter.
PMSG
Generator
Utility
Grid
Turbine
Wind
Speed
Filter
Gen. Side
Converter
Grid Side
Converter
Fig. 9: PMSG wind energy system.
3.1 Modeling of the Wind Turbine
The power coefficient (Cp) depend on the tip-speed
ratio (λ) and the pitch angle (β), and it can be
calculated for both fixed and variable speed wind
turbine by equation (1) [21] by:
(1)
where C1 to C6 are [0.5176, 116, 0.4, 5, 21, 0.0068].
The peak value of Cp is obtained at β =0° and λopt.
As stated in equation 1 the coefficient of
performance for this turbine depends on the tip
speed ratio λ and pitch angle β with 6 constants (C1
to C6)
3.1.1 Modeling of PMSG
The PMSG equations are given in d-q frame as [22]:
(2)
(3)
(4)
Where and are the direct and quadrature
components of the stator voltage, is the stator
resistance, and are the direct and quadrature
components of the stator currents, and are
the direct and quadrature components of the stator
self-inductance, is the electrical angular speed,
and is the permanent magnet rotor magnetic
flux, while the grid voltage are given in the (d-q)
frame that is rotating with the angular frequency
by:
(5)
(6)
Where is the filter resistance which is located
between the grid side converter and the grid, and
are the direct and quadrature components of the
grid side converter output currents, and are
the direct and quadrature components of the filter
inductance, and is the maximum grid phase
voltage.
3.1.2 Generator Side Converter Control
Its objective is to control the speed of the PMSG by
Field oriented control (FOC) for achieving variable
speed operation with maximum power point
tracking control. This controller consists of three PI
controllers; the rotor speed controller while the
others controller for direct and quadrature axis
currents.
3.1.3 Grid Side Converter Control
This controller’s aim is to control the reactive power
fed to the utility and the DC link voltage. Also, FOC
controller is applied to the grid side converter. This
controller requires 4 PI controllers, two for the
currents while the others for the reactive power and
DC link voltage.
3.2 Simulation Results
Simulation is done for 1.5 MW PMSG using
MATLAB/SIMULINK as depicted in Figure 10, the
parameters’ values of PMSG are listed in [23, 24].
By multiplying the base value with the PU value,
the actual value can be gotten. Here are the base
values [23]:
Where the subscript “b” means the base value; I,
V, P, f are the current, voltage, power, and
frequency, respectively; Z, L, C are the impedance,
inductance and capacitance, respectively; ω, ωm are
the electrical and mechanical angular frequencies,
respectively; T is the torque; J, K are the inertia and
stiffness, respectively; p is the number of pair poles
pairs; and ψr is the amplitude of the rotor flux. The
parameters of the wind energy conversion system
PMSG are listed in Table A.
3.2.1 Testing the Controllers with a Step Change
In the simulation, at the 10th second the speed is
changed, once from 10 to 12 m/sec. then reduced
after 10 sec. to be 8 m/sec. The DC link voltage
setpoint is 1500 v. The PMSG simulation results
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using PI and Fractional order PI [25] controllers
obtained by the GWO is compared to each other.
Equation (7) presents the cost function.
(7)
Where is the reference value for the DC
link voltage and is the reference for the
electrical angular speed.
Table 4. Transient response obtained by PI and
FOPI controllers.
the rotor speed (
PI
FOPI
Maximum percent overshoot (%)
2.35
0.39
Maximum percent undershoot (%)
6.5
1.07
Settling time after the overshoot (sec.)
5.76
4.00
Settling time after the undershoot (sec.)
6.21
4.15
DC voltage (Vdc)
PI
FOPI
Maximum percent overshoot (%)
1.2
0.87
Maximum percent undershoot (%)
1.7
1.43
Settling time after the overshoot (sec.)
4.6
4.03
Settling time after the undershoot (sec.)
5.62
5.30
Fig. 10: The simulation for 1.5 MW PMSG using MATLAB/SIMULINK
Figure 11 shows the rotor speed profile in PU with
PI and FOPI controllers parameters obtained using
GWO, the graph is started at 8 sec to neglect the
starting period transients. It can be noticed from
Figure 11 and Table 4 that the speed results using
FOPI controller has the lower overshoot percent of
0.39 % with faster settling time of 4.0 sec. when it is
compared to traditional PI controller which is being
used, the PI controller has an overshoot percent of
2.35 % with slower settling time of 5.76 sec, so it
has slower response than the FOPI response. for the
second disturbance for the system “the undershoot”,
it can be noticed that the maximum percent
undershoot using the FOPI controller tuned by
GWO, is smaller (1.07%) compared to its
counterpart PI controller (6.61%), also FOPI has a
faster settling time of 4.15 sec. compared to the PI
controller, which its settling time was 6.21 sec.
The DC link voltage is shown in Figure 12, its set
point value is 1500v. From Figure 12 and Table 4, it
can be noticed that The DC link voltage response
settles faster with the FOPID controller with 4.03
sec. FOPI controller has lower overshoot of 0.87%
compared to the PI controller which has an
overshoot of 1.2% and settling time of 4.60 sec. For
the second disturbance of undershoot occurrence, it
is noticed that the maximum percent undershoot,
obtained using the FOPI controller is smaller which
has a value of 1.43% and faster in its settling time
with 5.3 sec., if it compared with the rival values
obtained by the PI controller tuned with GWO
which has an under
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shoot of 1.7% with larger settling time of 5.62 sec.
The less maximum overshoot and settling time
responses of the generator speed and DC link
voltage obtained by the FOPI controller improves
the low voltage ride through capability of the PMSG
wind system.
Fig. 11: The rotor speed (ωr), in per unit, response obtained using PI and FOPI contro
llers.
Fig. 12: The DC voltage (v.) response obtained using PI and FOPI.
High frequency ripples in the DC voltage (Figure
12) caused by the harmonics associated with the
machine (generator) side rectifier.
3.2.2 Testing the Controller Performance with
Symmetrical Three Phase Fault
The PMSG model is tested with a disturbance of
symmetrical three phase to ground fault for a
duration of 5 cycles, which has been occurred at the
instant of 10 sec. In fault cases, there unbalance in
power between the load and the generated one will
accelerate the rotor speed as depicted in Figure 13.
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Fig.13: the speed after symmetrical three phase
short circuit
It can be noticed, form Figure 13 that both
controllers have the same overshoot percent may
due to that both rotor has the same kinetic energy
stored, at the fault the enegizes with the same
amount of energy, but PI controller has here the
lower settling time than usual in FOPI controller.
Figure 14 shows the DC link voltage response, that
wind turbine PMSG retrieves its initial (sepoint)
value rapidly, with lower overshoot for the FOPI
controller parameters tuned by GWO compared to
the PI controller.
Fig. 14: The DC voltage (v.) profile obtained by PI
and FOPI controllers after the symmetrical fault
occurrence.
Symmetrical fault Three phase fault stating at 10
sec. and lasts for 5 cycles (i.e. the periodic time is
20 msec. so the fault clearing occurred at 10.1 sec.)
at the grid side converter
The DC link voltage dropped to zero voltage which
may cause the wind turbine to be forced outage
from the network, the overshoot caused by the PI
reached to a high value 21.33% while the overshoot
reached to 7.33%, but the settling time of the PI
controller was about 1.5 sec. while the FOPI
controller took 2.5 sec. to settle after the three phase
fault disturbance.
3.2.3 Testing the Controller Performance with
Asymmetrical Single Line to Ground Fault
Asymmetrical grid faults such as single line to
ground happen more often than the symmetrical
faults. During the asymmetrical grid fault, there will
be a negative-sequence voltage, which can lead to
second-order harmonics in the injected currents that
has an effect the DC link voltage.
The fault occurs at the instant of 10 sec. and lasts for
5 cyles as in the previous case, both DC link voltage
and speed are shown in Figures 15, 16 and 17.
Figure 15 shows the DC voltage after fault
occurrence. Ripples may be due to the asymmetrical
components of the single line to ground (phase A to
ground) the overshoot was 7.33% with settling time
of about 1.2 sec. for the conventional PI controllers,
while the overshoot caused by the FOPI controllers
was 1.33% and the voltage is settled directly after
fault clearing.
Figure 16 shows the speed after the asymmetrical
fault. There is an overshoot with a very small
amount, which means that this type of fault has no
significant effect on the speed curve, also, may be
due to the slowness of such mechanical system.
After zooming the speed profile at the instant of
fault occurrence, the PI controller has a higher
overshoot with larger settling time than its rival
FOPI controller system.
Fig. 15: The DC voltage (v.) response obtained by PI
and FOPI controllers after the asymmetrical fault
occurrence.
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Fig. 16: The rotor speed (ωr) response obtained by
PI and FOPI controllers after the asymmetrical fault
occurrence.
Fig. 17: Zooming on the rotor speed (ωr) response
starting at 10 sec. obtained by PI and FOPI
controllers after the asymmetrical fault occurrence.
4 Conclusions
In this paper, a PID controller is introduced to
control the wind turbine PMSG. Also, the FOPID
controller is introduced, to obtain the better
optimization algorithm to be used in this paper for
PI and FOPI controller parameters optimization.
The performance analysis obtained from the PMSG
wind turbine using PI controller compared with it
rival FOPI in case of step changes in wind speed,
also, the system tested under abnormal conditions
such as symmetrical three phase to ground fault and
asymmetrical single line to ground fault.
APPENDIX A
Table A: The PMSG parameters
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