Journal of Technology Innovations in Renewable Energy, 2014, 3, 21-30
21
Optimal Design of PID Controller for Doubly-Fed Induction
Generator-Based Wave Energy Conversion System Using MultiObjective Particle Swarm Optimization
Adel A.A. Elgammal*
Utilities Engineering Department, The University of Trinidad & Tobago UTT, Point Lisas Campus, Esperanza
Road, Brechin Castle, Couva, Trinidad and Tobago
Abstract: This paper presents the complete modeling and simulation of Wave Energy Conversion System (WECS)
driven doubly-fed induction generator with a closed-loop vector control system. Two Pulse Width Modulated voltage
source (PWM) converters for both rotor- and stator-side converters have been connected back to back between the rotor
terminals and utility grid via common dc link. The closed-loop vector control system is normally controlled by a set of PID
controllers which have an important influence on the system dynamic performance. This paper presents a Multi-objective
optimal PID controller design of a doubly-fed induction generator (DFIG) wave energy system connected to the electrical
grid using Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). PSO and GA are used to optimize the
controller parameters of both the rotor and grid-side converters to improve the transient operation of the DFIG wave
energy system under a fault condition as compared with the conventional methods to design PID controllers.
Keywords: Grid integration, Wave Energy Conversion systems, Doubly-Fed Induction Generator (DFIG), Vector
control, Genetic Algorithm GA, Particle Swarm Optimization PSO.
I. INTRODUCTION
Producing energy from renewable energy resources
such as solar, wind, ocean, micro-hydro, biomass, etc
is becoming a necessity because of the the continuous
increasing of world energy demand. Since the
abundance of wave power potential and its pollutionfree nature, wave energy can be considered as one of
the attractive and green alternative energy sources in
the world today [1-7]. The Doubly Fed Induction
Generator (DFIG) is widely used in the development of
distributed renewable energy sources [8], [9]. The rotor
windings of the DFIG are arranged via the Rotor Side
Converter (RSC) to allow an AC current to be injected
by field orientation control to optimize the energy
conversion and keep the terminal voltage constant for
variable speed. The field orientation control based on
proportional, integral and differential controllers (PID
controllers) controls the active and reactive powers that
the DFIG exchanges with the electrical grid. The aim of
the field orientation control is to maximize the extracted
power from the wave [10-15]. Suitable controller
parameters highly improve system stability and
performance. However, the online tuning of these
parameters is difficult due to the nonlinearity and the
high complexity of the system [16]. “Differential
evolution (DE) is a population-based method and
generally considered as a parallel stochastic direct
*Address correspondence to this author at the Utilities Engineering
Department, The University of Trinidad & Tobago UTT, Point Lisas Campus,
Esperanza Road, Brechin Castle, Couva, Trinidad and Tobago; Tel: (868) 6428888 Ext. 32334; Fax: (868) 636-3339;
E-mail: adel_elgammal@ieee.org
E-ISSN: 1929-6002/14
search optimizer which is very simple, precise, fast as
well as robust algorithm” [17-19]. The DE can solve
optimization problems with non-linear and multi-modal
objective functions. Recently, intelligent optimization
algorithms such as genetic algorithms (GAs), tabu
search algorithm, simulated annealing (SA) and particle
swarm optimization (PSO) have been successfully
used as optimization tools in various applications,
including the online tuning of the controller parameters
[20-26]. “Particle Swarm Optimization (PSO) is an
evolutionary computation optimization technique (a
search method based on a natural system) developed
by Kennedy and Eberhart” [27-30].
In this paper, number of fitness functions is defined
to measure the performance of the proposed
controllers. The proposed objective functions are
designed to monomoze the over-current in the rotor
circuit, to minimize losses as well as optimal power
utilization. “Multi-objective optimization is used to find a
Pareto front which is a set of acceptable solutions for
conflected objective functions” [31-33]. MOPSO is used
to determine the optimal gains for the PID controllers to
both the stator-side converter and the rotor-side static
converter of the DFIG. For the purpose of comparing
the improvement obtained in the system dynamic
performance with the application of the MOPSO
procedures to design the controller gains, these results
are compared with those obtained using the MultiObjective Genetic Algorithm (MOGA). A complete
simulation model is developed for such machine under
variable speed operation using MATLAB Simulink
© 2014 Lifescience Global
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Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1
environment. Simulation results show that the
proposed design approach is efficient to find the
optimal parameters of the PID controllers and therefore
improves the transient performance of the WECS over
a wide range of operating conditions.
II. MODELING OF THE STUDIED SYSTEM
Figure 1 shows the proposed model for DFIG
converting power from the wave to deliver power into
the electric grid for a large range of wave variation. The
stator of the DFIG is directly connected to the electric
grid, whilst the rotor winding is fed through the back-toback PWM voltage-source inverters with a common DC
link via slip rings to control the voltage applied to the
rotor to allow DIFG to operate at a variety of speeds in
response to wave changes. The rotor-side converter
was implemented to provide an active and reactive
power control by the field-oriented current control, as
shown in Figure 2. The reactive power can be
Adel A.A. Elgammal
controlled by controlling the d-axis rotor current. The
stator active power Ps can be independently controlled
by controlling the q-axis rotor current. Figure 3 shows
the overall control scheme of the grid-side converter.
The grid-side converter is implemented to keep the dclink voltage constant regardless of the magnitude and
direction of the rotor power. The control of the grid-side
converter are organized in two loops; a DC-link current
control loop, which controls the current through the grid
filter, and DC-link voltage control loop that controls the
dc-link voltage.
III. DIGITAL SIMULATION RESULTS
The proposed MOPSO strategy has been tested for
validation using the DFIG whose ratings are given in
the Appendix. The wave model of Figure 4 is adopted
to generate a specific power reference and validate the
good power tracking performances and therefore
confirm the effectiveness of the proposed control
Figure 1: Schematic representation of Wave energy converter with Doubly-Fed Full-Controlled Induction Generator.
Figure 2: Rotor-side converter control.
Optimal Design of PID Controller for Doubly-Fed Induction
Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1
23
Figure 3: Stator-side converter control.
Figure 4: The wave model.
strategy based on MOPSO. To compare the
improvement obtained in the system dynamic
performance with the application of the MOPSO
procedure to design the controller gains, these results
are compared with those obtained using the MOGA.
For the same operation condition, the MOGA and
MOPSO were used to obtain the optimal gains for the
controllers of the stator-side and the rotor-side
converters.
In the GSC and the RSC control loops, there are
four PID controllers and each of them has a
proportional gain, an integral and differential gains. The
behavior of the converter depends on the control
system. If the controllers are tuned properly, it is
possible to improve the GSC and RSC converter’s
performance during the transient disturbances. The
MOGA and the MOPSO algorithms are applied to find
automatically the optimal parameters of the GSC and
the RSC controllers. The objective of the MOGA and
the MOPSO is to find the optimal parameters of the
four PID controllers, namely, four proportional gains
(KP1, KP2, KP3, and KP4) , four integral gains (KI1,
KI2, KI3, and KI4) and four differential gains (KD1,
KD2, KD3, and KD4) to optimize some fitness
functions.
The following objective functions were used to
measure the quality of the gains tuning to improve the
system performance during the transient disturbances.
These functions are represented by the weighted sum
of the Normalised Mean Square Error (NMSE)
deviations between output plant variables and desired
values. The NMSE deviations between output plant
variables and desired values are defined as:
24
Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1
J1 = NMSEVDC
(V V
=
(V
DC
DC ref
DC ref
J 2 = NMSE IDC
( I I
=
( I
DC
(
(
r
r ref
r ref
J 4 = NMSEQs
(Q Q
=
(Q
s
)
)
)
)
1
6.
Check the Pareto optimality of the multi-objective
fitness values of each particle. All non-dominated
solutions are saved in the Pareto archive
(external file)
7.
The global gbest particle is randomly selected.
8.
The velocity of each particle is updated using the
following equation.
2
(3)
2
(4)
2
t
(
Save the multi-objective fitness value of each
particle in vector form. These vectors store the
values of each gain of the PID controller. These
values are copied in the pbest vectors.
(2)
The SOPSO finds a single optimal solution of the
following objective function (Jo) which combines
several objective functions using specified or selected
weighting factors:
Jo =
5.
2
2
)
and the WECS-DFIG model is simulated to
obtain the values of the objective functions.
(1)
2
sref
sref
)
2
2
DC ref
DC ref
J 3 = NMSE r =
)
)
Adel A.A. Elgammal
)
J1 + 2 J 2 + 3 J 3 + 4 J 4 dt
(5)
Vid = Vid + C1 rand1
(P
pd
)
(
X id + C2 rand2 Prd X id
)
(7)
Where Pid, Pad are randomly chosen from the Pareto
archive, is the inertia factor, Vi,d is the velocity of the
particle i in the d_th dimension, c1 and c2 are weights.
0
Where 1 = 0.25, 2 = 0.25, 3 = 0.25, 4 = 0.25 are
selected weighting factors. J1, J2, J3, J4 are the selected
objective functions. The weighting factors in the
objective function (Jo) are used to satisfy different
design requirements. If a large value of 1 is used, then
the objective is to minimize the error of the DC link
voltage.
9.
X id = X id + Vid
Evaluate the quality of each particle. If the fitness
value of the particle is non-dominated, save it
into the Pareto archive. In the Pareto archive, if a
particle is dominated by a new one, then discard
it.
11.
Then, the new gbest is randomly selected. Two
Pareto solutions are chosen randomly for
Pr,d , Pi,d from the Pareto archive.
12.
Repeat the cycle, steps (8) to (11), until the
predetermined maximum number of generations
is reached or convergence is reached based on
some desired single or multiple criteria.
Initialize the population of the particle swarm with
random values of gains which are restricted by
the following minimum and maximum values:
K P min K P K P max
K Im in K I K Im ax
(6)
K D min K D K D max
2.
The feasibility of each particle is checked to
make sure the particle satisfies the constraints.
3.
All particles are initialized with random velocities.
4.
The objective functions are used to evaluate the
fitness of each particle in the swarm. The PID
controller gains are assigned for each individual
(8)
10.
The main steps of the the optimal PID controller
gains design procedure using MOPSO is an iterative
scheme involving the following steps:
1.
The position Xi,d of each particle is also updated
using the following equation to maintain the
particles within the feasible solution region.
In the calculation of the optimal gains by the GA and
the PSO procedures, the objective is to improve the
overall dynamic performance of the DFIG when it is
subjected to severe electrical disturbances and faults in
the electrical network. The dynamic simulations were
carried out for a three phase short circuit next to the
DFIG bus at time t = 0.2 s, lasting for 0.2 s. The gain
values for the PSO and GA adjustment procedures are
Optimal Design of PID Controller for Doubly-Fed Induction
Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1
25
Table 1: Gains Adjustments for the PID Controllers of GSC and RSC Converters Using PSO and GA
SOGA
SOPSO
MOGA
MOPSO
KP1
14.1873
8.5814
11.0665
14.8185
KI1
1.0937
2.2297
1.6190
2.6380
KD1
0.5205
0.9560
1.0463
1.4554
KP2
13.5941
11.9220
12.7491
9.3607
KI2
1.1020
1.5187
1.1730
1.6929
KD2
0.2522
1.0467
1.6869
0.7970
KP3
12.3800
12.6762
15.8444
18.4986
KI3
0.9673
1.0840
0.9978
1.4495
KD3
0.1949
0.9218
0.5987
1.0303
KP4
6.8077
11.9575
13.0007
10.2206
KI4
1.7054
1.8599
2.3141
3.5095
KD4
0.4762
0.8695
1.1065
1.1325
presented in Table 1. The oscillations of the dc-link
voltage, when applying the MOGA are slightly larger
than when applying the MOPSO, as shown in Figure 5.
However, the dc-link voltage oscillations in both
designs do not affect the continuous operation of the
WECS and consequently improving the DFIG dynamic
performance. The grid-side converter current is shown
in Figure 6-a, a reduction in the over-current can is
easily be observed, when the gains are adjusted by the
MOPSO as compared with those adjusted via MOGA,
consequently contributes towards maintaining the
converter in operation during the fault period. The gridside converter voltage dynamic behavior is shown in
Figure 6-b. It is observed that with the use of gains
obtained by MOGA the terminal voltage presents
deeper sag as compared with those controllers with
Figure 5: DC Link Voltage.
gains adjusted by the proposed MOPSO procedure.
Figure 6-c presents the grid side converter active
power behavior. It is observed that in the case when
controllers with gains adjusted by MOPSO are used,
the active power presents smaller oscillations as
compared with the MOGA. Figure 6-d shows a
reduction in the reactive power injected into the
electrical network by the grid-side converter in case the
controllers’ gains are adjusted by the MOGA and
MOPSO procedures. This implies that the transient
performance of the WECS is improved using MOGA
and MOPSO. Figure 7-a shows the rotor side converter
voltage, where it can be observed that the over-voltage
in the rotor circuit is reduced when the controllers’
gains are those obtained with the MOGA and MOPSO
procedures. Figure 7-b presents a reduction on the
26
Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1
Adel A.A. Elgammal
Figure 6: Grid Side Converter transient performance during the fault period.
(a) Grid Side Converter Current. (b) Grid Side Converter Voltage. (c) Grid Side Converter Active Power. (d) Grid Side Converter
Reactive Power.
Optimal Design of PID Controller for Doubly-Fed Induction
Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1
27
Figure 7: Rotor Side Converter transient performance during the fault period.
(a) Rotor Side Converter Current. (b) Rotor Side Converter Voltage. (c) Rotor Side Converter Active Power. (d) Rotor Side
Converter Reactive Power.
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Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1
Adel A.A. Elgammal
Table 2: System Dynamic Behavior Comparison
SOGA
SOPSO
MOGA
MOPSO
RMS Stator Voltage (PU)
0.9906
0.9943
0.9955
0.9987
RMS Rotor Voltage (PU)
0.1838
0.1901
0.1969
0.1974
RMS Stator Current (PU)
0.7213
0.7555
0.7229
0.7355
RMS Rotor Current (PU)
0.1707
0.1706
0.1775
0.1748
Maximum Transient Stator Voltage
Over/Under Shoot (PU)
0.0689
0.0609
0.0622
0.0507
Maximum Transient Stator Current –
Over/Under Shoot (PU)
0.0924
0.0980
0.0967
0.0862
Maximum Transient Rotor Voltage
Over/Under Shoot (PU)
0.0721
0.0779
0.0681
0.0620
Maximum Transient rotor Current –
Over/Under Shoot (PU)
0.0980
0.0868
0.0986
0.0807
NMSEVDC
0.0847
0.0671
0.0614
0.0519
NMSEr
0.0912
0.0949
0. 0899
0.0845
NMSEIDC
0.0612
0.0669
0.0675
0.0504
NMSEQs
0.0669
0.0863
0.0961
0. 0789
THDGSV (%)
0. 0625
0.0518
0.0971
0.0602
THDGSI (%)
0.0966
0.0847
0.0845
0.0778
THD RSV (%)
0.0725
0.0799
0.0834
0.0689
THD RSI (%)
0.0868
0.0825
0.0764
0.0739
Generator Efficiency (PU)
0.8557
0.8577
0.8772
0.8842
Generator Power Factor
0.9859
0.9814
0.9997
0.9985
rotor side converter current oscillation when the gain
adjustments are accomplished by the MOPSO as
compared to the result with the MOPSO technique.
Figures 7-c and 7-d illustrate the dynamic response of
both rotor side converter active and reactive powers,
for the cases of gains adjusted by MOPSO and by the
MOGA procedures. It could be easily concluded that
the proposed control strategies based on MOGA and
MOPSO achieve satisfactory dynamic performances.
Table 2 shows the system behavior comparison using
the SOGA, SOPSO, MOGA and MOPSO based Self
tuned controllers. The table illustrates the total
harmonic distortion measurement in the three phase
grid voltage waveforms, three phase grid current
waveforms, three phase rotor voltage waveforms and
three phase rotor current wave forms. The system
produces less than 10% voltage and current THD
which is compliant to IEC 6100-3-2.
IV. CONCLUSION
This paper has presented the modeling and
simulation of wave energy driven doubly-fed induction
generator which is connected to the utility grid. The
stator of the DFIG is directly connected to the AC
mains, whilst the rotor winding is fed through the backto-back PWM voltage-source inverters with a common
DC link via slip rings to control the voltage applied to
the rotor to allow DIFG to operate at a variety of
speeds in response to wave changes. The PID
controllers are used to control both GSC and RSC
converters and their parameters are optimally designed
using the particle swarm optimization (PSO) algorithm
and Genetic Algorithm (GA). Simulation studies are
carried out and compared the results obtained with the
proposed optimal PID controller parameters design
using MOPSO with those using controllers adjusted by
the MOPSO. Results show that the proposed design
approach is efficient to find the optimal parameters of
the PID controllers and improves the transient
performance of the wave energy system over a wide
range of operating conditions. THD levels of the
converter output voltage has been estimated using fast
Fourier transform which satisfies the IEEE 519-1992
standard.
Optimal Design of PID Controller for Doubly-Fed Induction
Journal of Technology Innovations in Renewable Energy, 2014, Vol. 3, No. 1
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DFIG Parameters
Nominal power, Pbase = 660 KW
Grid frequency, f = 60 Hz
Nominal voltage (L-L), Vbase = 400 V
Stator resistance, rs = 0.03513 pu
Stator inductance, Lls = 0.04586 pu
Rotor resistance, rr = 0.03488 pu
Rotor inductance, Llr = 0.04586 pu
Mutual inductance, Lm = 1.352 pu
Pole pairs, P = 2
WEC Parameters
H = 0.726 m, T = 5.612 s, d =1 m, = 0.120 m,Vp =
500 V.
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Received on 28-12-2013
Accepted on 05-03-2014
Published on 25-03-2014
DOI: http://dx.doi.org/10.6000/1929-6002.2014.03.01.4
© 2014 Adel A.A. Elgammal; Licensee Lifescience Global.
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