A Comparative Analysis on Proportional-Integral and Fuzzy-Logic
Control Strategies for Doubly-Fed Induction Generators
ANKINEEDU PRASAD PADAMATA1,*, GUDAPATI SAMBASIVA RAO2
1Electrical and Electronics Engineering,
Dr. YSR ANU College of Engineering & Technology,
Acharya Nagarjuna University,
Nagarjuna Nagar, Guntur - 522 510, Andhra Pradesh,
INDIA
2Department of Electrical & Electronics Engineering,
R.V.R. & J.C. College of Engineering,
Guntur - 522 019, Andhra Pradesh,
INDIA
*Corresponding Author
Abstract: - This research investigates superior control methods for optimize the performance of Doubly-Fed
Induction Generators in wind energy conversion systems. This proposed work, compares the well-established
Proportional-Integral controller, with a Fuzzy Logic controller, known for its effectiveness in managing non-
linear systems. To achieve a thorough analysis, this research develops a detailed mathematical model,
specifically adopted to the DFIG system. It employs a PI controller for both the rotor-side and grid-side
converters of the DFIG system. To enhance performance, a Fuzzy Logic controller is introduced to replace the
PI controller, based on real-time operating conditions and gain values. Extensive simulations evaluate
rigorously various performance metrics of the DFIG system under different control strategies. This analysis
provides valuable insights to guide the selection of optimal control techniques, for wind energy systems using
DFIGs. The analysis contributes to advancements in reliability, and efficiency for DFIG-based wind-energy
systems, furthering the development of sustainable energy solutions.
Key-Words: - Control strategies, DFIGs, PI controller, Fuzzy-Logic Controller (FLC), mathematical model,
wind energy systems, performance metrics, efficiency.
Received: April 9, 2023. Revised: February 4, 2024. Accepted: March 17, 2024. Published: April 16, 2024.
1 Introduction
There has been a significant rise in interest
surrounding wind energy conversion systems.
Amidst the array of wind power generation
techniques, DFIG distinguishes itself with its
enhanced energy transfer capability, cost efficiency,
and, adaptable control features, [1].
Wind turbines, devices converting wind kinetic
energy to electrical energy, come in various types-
“horizontal”, “vertical”, “constant” and “adjustable”
speed generator, and varying blade numbers, [2].
DFIG, a variable-speed generator, minimizes losses
by recuperating slip power in both sub-synchronous
and hyper-synchronous modes, enhancing efficiency
across a broad range of wind speeds. Achieving this
involves a tandem AC-DC-AC converter on the
rotor circuit. Additionally, the stator's direct grid
connection ensures the converter handles only a
minimal portion of overall output power
(approximately±30%), eliminating the necessity of
expensive full-scale converter, [3].
Diverging from traditional generators, DFIG
incorporates a sequence “voltage-source converter”
for the wound-rotor. The inclusion of converters
with feedback, specifically the in rotor-side, and
grid-side, enhances DFIG's control capabilities, and
stability, surpassing those of other generators.
A prevalent DFIG control technique is vector
control, employed on the “RSC”, for independent
control of real. and responsive power. This can be
achieved by decoupling the rotor currents, into two
components, akin direct, and quadrature, managing
the real, and responsive power respectively, [4].
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The control strategy, established in the
traditional PI control-technique, involves controllers
for , , , and , ensuring optimal
power monitoring, stator terminal voltage-
regulation, DC voltage level, and responsive power
level at GSC, [5]. Despite conventional use of PI
controllers, their limitations in robustness and
tuning have prompted exploration of alternative
control methods, [6].
Studies have explored the dynamic behavior of
DFIG, from transient stability models, [7], to
detailed grid-connected DFIG models, [8]. Modal
analysis, addressing changes in modal
characteristics under various operating scenarios,
and system specifications, has also been explored,
[9]. Prior works on delink control of real, and
responsive power for DFIG, have been illustrated,
[10].
In this paper, by recognizing PI controller
shortcomings, a Fuzzy Logic Controller (FLC) for
DFIG is proposed. Fuzzy control has found
application in various wind-turbine controls,
comprising of swift control, pitch-control, MPPT,
and extracted power control, [11], [12], [13], [14].
The fuzzy logic approach provides a non-linear,
model-free control approach, suitable for
coordinated RSC, and GSC control in DFIG system.
While “Mamdani-type” controllers may have
limitations, a “Takagi-Sugeno” (TS) type fuzzy
controller provides a broader scope of control gain
adjustment. It is emphasized the implementation of
TS fuzzy controllers for regulating real power
output, and DC capacitor voltage in DFIG,
demonstrating its effectiveness in suppression of
rotor speed oscillations, and regulating DC voltage
fluctuations, [15].
In line with current grid codes, wind farms must
withstand system faults, necessitating ability to ride
through faults. The effectiveness of TS-fuzzy
controllers on DC voltage variation, and rotor speed
oscillations, evaluating the impact on improving the
system's fault ride-through capability, [16].
The implementation of a tandem connected AC-
DC-AC converter for DFIG's integration into the
grid underscores the importance of power electronic
converters. Operating with a fraction of the overall
system power, these converters hold promise for
minimizing losses in contrast to direct-driven
synchronous generators, [17]. Within this
investigation, two controller types are introduced:
proportional-integral (PI) for governing real power
through torque control and Fuzzy-PI for managing
speed control.
2 System Model
2.1 DFIG Model
Being the variable-speed nature of the DFIG, its
stator connects straightforwardly to the grid, via an
isolation-transformer, delivering the majority of
power. Simultaneously, the rotor links via a tandem
AC-DC-AC converter, enabling slip power
recuperation. The converter in this study includes
two tandem VSCs (1-RSC and 2-GSC) with a
capacitor establishing a DC bus. With an effective
control approach, the tandem converters facilitate
mutual power transmission, governing real, and
responsive power, [18].
2.2 Rotor Side Controller
During the initial phase, rotor current references
and are computed based on the
real (), and responsive () reference
powers. These are then compared with and
. Differences are computed using two PI
controllers, generating dq reference voltages, =
(, ). These are transformed to the rotor's
synchronous reference and applied through a PWM
modulator, [19]. The control system equations are
given in (1) to (5).
=
(1)
=
(2)
=( )(
)+
=( )(
)+ (3)
= (
) (4)
= (
)+(
) (5)
Where and symbolize coupling residues.
2.3 Controller Gain Design for
In this article, a current loop model is utilized to
determine the appropriate gains of the PI controller,
simplifying the power loop used [20]. This approach
reduces the system's complexity, as it employs the
direct power control technique.
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idqr
1
σLrs+Rr
s
ki_idqr
kp_idqr+
idqr_ref +
-
V*dqr
Fig. 1: PI Controller for
The PI control scheme for the control current is
shown in Figure 1. The gain is described by,
=
(6)
=
(7)
Where ω= Natural angular frequency
ω = 100/
= Leakage factor
= Stator-referred rotor inductance
= Stator-referred rotor resistance
= Rotor Time constant
=
2.4 Speed Controller Gains
p
J s
s
ki_n
kp_n
+
SpeedΩn_ref +
-SpeedΩn
Fig. 2: PI controller implemented for Speed control
The Figure 2 shows the speed control loop with
PI controller which is implemented in the DFIG
system. The proportional constant for speed
controller is given by the following equations:
=
(8)
= ω
(9)
Where ω=
= Natural angular frequency =
0.05)
= Moment of Inertia
p= Pair of poles
2.5 PI Controller in GSC
The voltages on the grid side in the dq coordinate
framework are expressed as follows:
=
(10)
=
(11)
= (12)
= (13)
idqg
1
Lgs+Rg
s
ki_idqg
kp_idqg+
idqg_ref +
-
V*dqg
Fig. 3: PI Controller implemented in PI Controller
The Figure 3 shows the grid currents control
loop in GSC. Here the gains and are
described by the following equations:
=2ω (14)
= ω
(15)
Where = 2πf
= Inductance of the grid-filter
= Resistance of the grid-filter
=
2.6 PI Controller in DC Link
1
C s
s
ki_vdc
kp_vdc
+
V*dc +
-Vdc
Fig. 4: PI controller implemented in DC link
The Figure 4 shows the PI Controller
implemented in DC link. The control equation can
be expressed as follows. Here the gains , and
can be described by the equations (17) and
(18).
(16)
= 2Cω (17)
= C ω
(18)
It is observed that the DC link potential can be
regulated by adjusting the real power. Additionally,
the DC bus potential is influenced by the external
current flowing into the converter's DC bus.
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3 Fuzzy Controller
The Fuzzy Logic Controller (FLC) is recognized for
its ability to adapt to nonlinear systems through the
incorporation of human knowledge and expertise in
decision-making. This proposed investigation
emphasizes on implementing the “FLC” due to its
“robustness”, and “effectiveness” in managing
nonlinear systems. “Mamdani” model is opted due
to its capacity to retain Optimization as emphasized,
[21]. Implementing this controller would be a
straightforward role. Separate FLC controllers are
employed in conjunction with vector control scheme
of the RSC. First is designated to regulate the
which corresponds to the orientation of the stator
flux vector in space. The arrangement ensures that
the is directly related to the produced responsive
power. Second is employed for regulation of the
“ which is directly related to the evolved
electromotive-torque. This configuration enables
speed-regulation, and accordingly the control over
produced real power, [22]. The architecture diagram
of FLC is shown in Figure 5.
DECISION
MAKING LOGIC DEFUZZIFICATION
RULE BASE
RULE BASE
FUZZIFICATION
INPUT
FUZZY INTERFACE
Fig. 5: Architecture of FLC
3.1 Fuzzy Controller to DFIG
Fuzzy theory constitutes a numerical control
algorithm founded on principles derived from Fuzzy
set-theory, Fuzzy-linguistic-variables, and Fuzzy
logic. Adjustments are made to the rules and
membership functions in a manner that enhances the
efficacy of the FLC. The membership functions are
configured to position them in proximity to the zero
region, aiming to enhance control performance.
Conversely, positioning them farther from the zero
region contributes to a quicker control response.
Enhancements in performance can be achieved
by modifying both the rules and membership
functions. Observing the response characteristics
such as rise time, settling time, and maximum
overshoot can be accomplished by systematically
varying the values of “ kp” & “ki” across multiple
iterations. The two inputs, error and change in error,
are characterized by seven variables each, including:
Tiny (T), Small (S), Petite (P), Normal (N), Grande
(G), Large (L), Enormous (E) so as to form a (7X7)
matrix for the Fuzzy rules as shown in Table 1.
Table 1. Rule base for MF in FLC
er/rs
T
S
P
N
G
L
E
T
TT
TS
TP
TN
TG
TL
TE
S
ST
SS
SP
SN
SG
SL
SE
P
PT
PS
PP
SN
SG
SL
SE
N
NT
NS
NP
NN
NG
NL
NE
G
GT
GS
GP
GN
GG
GL
GE
L
LT
LS
LP
LP
LG
LL
LE
E
ET
ES
EP
EN
EG
EL
EE
The gain attributes of the PI controller are
subjected to reconciliation through methods such as
trial and error or by employing the Ziegler-Nichols
tuning technique. The adjustment of the values for “
kp” & “ki” is carried out based on the Fuzzy
membership functions and rules implemented,
thereby constituting a Fuzzy controller. The rule
bases for tuning the values of “ kp” & “ki” are
specified in Tables.
Manually designing the Fuzzy Logic Controller
(FLC) involved employing an iterative approach.
Incorporating “membership-functions (MFs)” with
interims, that vary in span, are essential, with the
narrow interim approaching zero, to enhance
accuracy. In this framework, the suggested RSC
block utilizes a simple inherent speed regulation
approach. This strategy utilizes the recorded rotor
speed to generate a reference electromotive-torque.
The reference torque is intended to utilize in the “
” control, [19].
3.2 Fuzzy “” Control
In the control of DFIG, setting the reference to zero
is a typical practice, as implemented in this paper.
Indeed, the adjustment is made to diminish the
required rotor-currents, effectively restricting the
dimensioning of the rotor-windings, [23]. This
aspect similarly enables the restriction of the control
over responsive power-generation exclusively to the
Grid Side Converter. The employed regulator
utilized a Mamdani fuzzy-system with one input and
one output, featuring 7 MFs for incorporating both
input and output variables, [24].
3.3 Fuzzy “” Control
The system takes the error (er) as input and
produces the Control parameter (Ctr) as its output.
The details of MFs and rules are outlined in Figure
6, Table 2 and Table 3.
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Fig. 6: MF of for FLC
Table 2. MF Types and Range
_er
MF
Type
Range
T
Trapezoidal
[-50 -50 0 50]
S
Triangle
[0 50 100]
P
Triangle
[50 100 150]
N
Triangle
[100 150 200]
G
Triangle
[150 200 250]
L
Triangle
[200 250 300]
E
Trapezoidal
[230 270 320 350]
Ctr_vdr
T
Trapezoidal
[-140 -140 0 50]
S
Triangle
[0 50 100]
P
Triangle
[50 100 150]
N
Triangle
[100 150 200]
G
Triangle
[150 200 250]
L
Triangle
[200 250 300]
E
Trapezoidal
[250 270 330 350]
Table 3. Rule Table
_er
T
S
P
N
G
L
E
Ctr_vdr
T
S
P
N
G
L
E
Figure 7 shows the MF of for FLC and
Table 4 and Table 5, describes MF range and rule
base. Similarly, the FLC and rule base can be
implemented for
Fig. 7: MF of for FLC
Table 4. MF Types and Range
er
MF
Type
Range
T
Trapezoidal
[-160 -160 -82 -31]
S
Triangle
[-96.25 -32.5 31.25]
P
Triangle
[-32.5 31.25 95]
N
Triangle
[31.25 95 158.8]
G
Triangle
[95 158.8 222.5]
L
Triangle
[158.8 222.5 286.2]
E
Trapezoidal
[229 268.7 312 350]
Ctr_vdg
T
Trapezoidal
[-150 -150 -7 43]
S
Triangle
[-7.143 43.88 94.9]
P
Triangle
[43.88 94.9 145.9]
N
Triangle
[94.9 145.9 196.9]
G
Triangle
[145.9 196.9 248]
L
Triangle
[197.8 248.9 299.9]
E
Trapezoidal
[248 268 329 350]
Table 5. Rule Table
_er
T
S
P
N
G
L
E
Ctr_vdg
T
S
P
N
G
L
E
Figure 8 describes MF of Speed_er for FLC and
and Table 6 and Table 7, describes MF range and
rule base.
Fig. 8: MF of Speed_er for FLC
Table 6. Speed MF Types and Range
Speed_er
MF
Type
Range
T
Trapezoidal
[-50 -50 0 50]
S
Triangle
[0 50 100]
P
Triangle
[50 100 150]
N
Triangle
[100 150 200]
G
Triangle
[150 200 250]
L
Triangle
[200 250 300]
E
Trapezoidal
[230 270 320 350]
Ctr_idr
T
Trapezoidal
[-140 -140 0 50]
S
Triangle
[0 50 100]
P
Triangle
[50 100 150]
N
Triangle
[100 150 200]
G
Triangle
[151 201 251]
L
Triangle
[200 250 300]
E
Trapezoidal
[250 270 330 350]
Table 7. Speed_er Rule Table
Speed_er
T
S
P
N
G
L
E
Ctr_idr
T
S
P
N
G
L
E
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4 Comparative Analysis
The wind speed is held at 8m/s for the first 2
seconds. From 2 to 3 seconds, it increases to 9m/s.
The wind speed remains consistently at 10m/s from
3 to 4 seconds. Between 4 and 5 seconds, the wind
speed is set at 11m/s. From 5 to 6 seconds, the wind
speed is sustained at 12m/s, and from 6 to 7
seconds, it further increases to 13m/s shown in
Figure 9.
Fig. 9: Wind speed response
Fig. 10: Active Power extracted with DFIG
Fig. 11: Reactive Power Consumed by the DFIG
The power extraction is analyzed in both cases,
namely, with a PI controller and a Fuzzy controller.
The Figure 10 shows the active power extracted
from the wind and Figure 11 shows reactive power
consumed from the grid. In the context of reference
tracking ability, both FLC, and PI controller
demonstrate comparable performance, exhibiting
fluctuations of in steady state. Notably, the FLC
exhibits a faster settling time to the reference,
analyzed to the PI controller. This implies that the
FLC achieves the desired reference value more
rapidly and with reduced oscillations, illustrates its
superior transient response characteristics.
The faster settling time of the FLC suggests a
more agile and responsive control mechanism,
particularly beneficial in scenarios where quick and
accurate adjustments to the reference are crucial.
Although both controllers, achieve identical tracking
abilities, the nuanced disparity in settling-time
emphasizes the efficiency of Fuzzy-Logic Control in
promptly attaining, and, sustaining the desired
reference. This distinction emphasizes Fuzzy-Logic
Control's expertise at quickly reaching, and,
maintaining the desired reference, particularly when
compared to the PI controller. Table 8 shows the
power extracted with PI and FLC. The machine
name plate details are provided in Table 9.
Table 8. Active Power extracted from wind
Wind
DFIG
m/s
PI-Active Power in KW
FLC- Active Power in
KW
8
104
100
9
137.5
132.5
10
170.5
170
11
208.75
209.25
12
247.5
251.25
13
250.25
251.25
Table 9. DFIG name plate details:
Power(P)
250 KW
Stator Voltage (Vs)
400 V
Stator Current (Is)
370 A
Rotor Voltage (Vr)
400 V
Poles pair(p)
2
Frequency(f)
50Hz
Rotor speed (ω
1500 rpm/157.1 rad/s
DC Bus Voltage (Vdc)
600V
5 Conclusions
The paper presents a control-system designed for a
DFIG-based wind turbine, employing vector control
techniques. The study incorporates a comparative
analysis between a Mamdani FLC, and a PI
controller. The results indicate that, the FLC
exceeds the PI controller, exhibiting a quicker, and
more precise response. The implementation of FLC
results, in a higher electromagnetic torque reference,
causing a slightly elevated rotational rotor speed in
comparison to the PI controller.
This outcome indicates that, the improved
dynamic response, and efficiency of the FLC within
the structure of DFIG-based wind turbine control.
The paper recognizes the potential for further
advancements, emphasizing the importance of
exploring smarter control methods for improved
tuning of the FLC.
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This suggests a continuous interest in refining,
and enhancing, the control strategy to achieve better
performance, and maximize potential energy yield
in DFIG-based wind turbine systems.
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Contribution of Individual Authors to the
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Conflict of Interest
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WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2024.19.11
Ankineedu Prasad Padamata, Gudapati Sambasiva Rao
E-ISSN: 2224-2856
118
Volume 19, 2024
