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Comparative Study on the performance of Fuzzy-PID
and MRAC-PID Controllers based on DPC with SVM
for DFIG using MPPT Strategy
F. Amrane and A. Chaiba
LAS Research Laboratory
Department of Electrical Engineering.
University of Setif 1, Setif, Algeria.
E-mail : [email protected]; [email protected].
Abstract—In this paper, we realized a comparative study of
hybrid controllers Fuzzy-PID and MRAC-PID for doubly fed
induction generator (DFIG) based on Direct Power Control with
a fixed switching frequency proposed for wind generation
application. First, a mathematical model of the doubly-fed
induction generator written in an appropriate d-q reference
frame is established to investigate simulations. In order to control
the DFIG, active and reactive power controllers and space-vector
modulation (SVM) are combined to replace the hysteresis
controllers used in the original DPC drive, a control law is
synthesized using PID controllers. We proposed two new control
strategies for controlling the rotor current, the first based on
RMCA and the second based on FLC. The performance of each
of them is based on the DPC algorithm are investigated and
compared to those obtained from the PID controller. Results
obtained in environment show that the
regulation of rotor currents via MRAC strategy is relatively
improved compared to that using FLC, namely the power error
and the quality of energy injected into the grid.
Keywords—Doubly fed induction generetor (DFIG), Direct
power control (DPC), Model Reference adaptive control
(MRAC), Space vector modulation (SVM), Fuzzy logic control
(FLC), maximum power point tracking (MPPT).
I. INTRODUCTION
The development of wind energy has grown significantly due to the diversity of exploitable areas and to the relatively attractive costs. Many of the wind turbines installed today are equipped with double fed induction machine (DFIG). However, most of these machines are connected directly to the network to avoid the presence of a converter. [1-2].
A DFIG consists of a wound rotor induction generator (WRIG) with the stator windings directly connected to a three-phase power grid and with the rotor windings mounted to a bidirectional back-to-back IGBT frequency converter. A schematic diagram of variable speed wind turbine system with a DFIG is shown in Fig. 1.
Control strategies of DFIG have been discussed in
literatures [3-5]. Control of DFIG through the Field Oriented
Control (FOC) which is performed by rotor currents control has
been developed in [6]. FOC method depends on parameters
variation and its power dynamics can be influenced by these
variations. Although, DFIG control using Input-Output
Feedback Linearization method can operate below and above
synchronous speed, but complication of control method and
dependence on parameters are its disadvantages.
Direct power control (DPC) strategy, as an alternative, has
been introduced to the DFIG based wind power generation, the
basic theory of DPC has been described in detail in [7], same as
the well-known direct torque control strategy, the basic DPC
has the demerits of large torque and current ripple and variable
switching frequency, a space vector modulation based constant
switching frequency DPC method is proposed in [8] to solve
the previous problems, and some compensation method is
proposed as well to improve the system performance. Further,
three improved DPC methods, with different control targets, for
DFIG control system have been discussed and implemented in
[9], it shows that these three strategies can be used to regulate
the active and reactive powers independently under both
normal and grid voltage-dip conditions with different steady
state and dynamic performance.
This paper is organized as follows; firstly the modeling of the turbine is presented in section II. In section III, the mathematical model of DFIG is given. Section IV presents Direct Power Control of DFIG which is based on the orientation of the stator flux vector along the axis ‘d’.
Fig.1. Schematic diagram of wind turbine system with a DFIG.
Ωmec
Gearbox
DFIG
Power
Grid AC/DC DC/AC
Pem
The power Converter
machine Side
The power Converter Grid Side
MPPT DPC Cp_max
Préf
Qref=0
Vα Vβ
Sα Sb Sc
SVM
PWM
Sα Sb Sc
International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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In section V and section VI present Model Reference Adaptive Control and the model of Fuzzy logic control respectively, they are established to control the rotor currents after being compared by conventional regulators PID. In section VII, computer simulation results are shown and discussed. Finally, the reported work is concluded.
II. MODEL OF THE TURBINE
The wind turbine input power usually is:
(1)
Where is air density; is wind turbine blades swept area in the wind; is wind speed.
The output mechanical power of wind turbine is:
(2)
Where Cp represents the wind turbine power conversion efficiency. It is a function of the tip speed ratio λ and the blade pitch angle β in a pitch-controlled wind turbine. λ is defined as the ratio of the tip speed of the turbine blades to wind speed. is given by:
(3)
Where R is blade radius, Ωt is angular speed of the turbine. Cp can be described as [10-11]:
( ( )) [ ( )
( )]
( ) ( ) (4)
Fig.2. Power coefficient variation Cp
In our work we use the wind profile, as shown in fig. 3:
Fig.3. Wind profile (Wind Speed).
The maximum value of ( ) is achieved
for degree and for . This point
corresponds at the maximum power point tracking (MPPT) [16]
After the simulation of the wind turbine using this wind profile, we test the robustness of our MPPT, we have as results the curve of power coefficient versus time; this latter
achieved the maximum value mentioned in Fig.6 ( ) despite the variation of the wind
Fig.4. Power coefficient (Cp).
III. MATHEMATICAL MODEL OF DFIG
The generator chosen for the conversion of wind energy is
a double-fed induction generator, DFIG modeling described in
the two-phase reference (Park). The general electrical state
model of the induction machine obtained using Park
transformation is given by the following equations, [12-13]:
Stator and rotor voltages:
. (5)
. (6)
( ) . (7)
( ) . (8)
Stator and rotor fluxes:
(9)
(10)
(11)
(12)
The electromagnetic torque is given by:
( ) (13)
And its associated motion equation is:
0 2 4 6 8 10 12 140
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
X: 8.107
Y: 0.4785
Vitesse relative Lambda.
Coef
ficien
t de
puiss
ance
.
Cp
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.86
7
8
9
10
11
12
13
Time (Secondes).
Win
d S
pe
ed
.
Wind Speed (m/sec).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
Time (Secondes).
Pow
er C
oeffi
cien
t.
Cp
Cp_max=0.4785
=8.107
International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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(14)
(15)
where: is the load torque is total inertia in DFIG’s rotor, Ω
is mechanical speed and G is gain of gear box.
The voltage vectors, produced by a three-phase PWM inverter, divide the space vector plane into six sectors, as shown in Fig. 5 [14].
Fig. 5 The diagram of voltage space vectors in α-β plan.
In every sector, each voltage vector is synthesized by the basic space voltage vector of the 2 sides of the sector and 1 zero vector. For example, in the first sector, Vaβ is a synthesized voltage space vector and is expressed by:
(16)
After projection the vectors , and we have:
‖ ‖ ( )
(
√
√ )
(
√
√ )
(17)
‖ ‖ ( )
(
√
√ )
(18)
(√ √ )
(19)
√
(20)
IV. DIRECT POWER CONTROL OF DFIG
In this section, the DFIG model can be described by the
following state equations in the synchronous reference frame
whose axis d is aligned with the stator flux vector as shown in
fig. 6, ( )and ( ) [7].
By neglecting resistances of the stator phases the stator
voltage will be expressed by:
(21)
Fig. 6 Stator and rotor flux vectors in the synchronous d-q Frame.
We lead to an uncoupled power control; where, the
transversal component irq of the rotor current controls the
active power. The reactive power is imposed by the direct
component ird as in shown in Fig. 7:
(22)
(23)
The arrangement of the equations gives the expressions of
the voltages according to the rotor currents (Fig. 5):
(
)
(
) (24)
(
)
(
)
(25)
(26)
(
)
(27)
with:
(28)
where:
are stator flux components, are rotor flux
components, are stator voltage components,
are rotor voltage components. are stator and rotor
resistances, are stator and rotor inductances, is
mutual inductance, is leakage factor, is number of pole
pairs, is the stator pulsation, is the rotor pulsation, is
the friction coefficient, and are stator and rotor time-
constant, and is the slid.
Stator Axis: Is fixing
Rotor Axis
d-q Frame
θr
θs
0
θm
Sector1 Sector3
Sector4 Sector6
Sector5
β
α
Sector2
V2 (110) V3 (010)
V4 (011)
V5 (001) V6 (101)
V1 (100)
V0 (000)
V7 (111)
Vαβ
T1/Ts*V1
T2/Ts*V2
International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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Fig. 7 The doubly fed induction generator simplified model.
V. MODEL REFERENCE ADAPTIVE CONTROL
The system studied in this paper is based on a first-order linear
plant approximation given by [15-17]:
( ) ( ) ( ) (29)
where x(t) is the plant state, u(t) is the control signal and a and
b are the plant parameters. The control signal is generated
from both the state variable and the reference signal r(t),
multiplied by the adaptive control gains K and Kr such that
( ) ( ) ( ) ( ) ( ) (30)
where K(t) is the feedback adaptive gain and Kr(t) the feed
forward adaptive gain. The plant is controlled to follow the
output from a reference model
( ) ( ) ( ) (31)
where is the state of the reference model and and
are the reference model parameters which are specified by the
controller designer. The object of the algorithm is for
→0 as →∞, where is the error signal. The
dynamics of the system may be rewritten in terms of the error
such that
( ) ( ) ( ( )) ( )
( ( )) ( ) (32)
Using Equations (27), (28) and (29), it can be seen that for
exact matching between the plant and the reference model, the
following relations hold
(33)
(34)
Where (K) E
denotes the (constant) Erzberger gains [18].
Equations (33) and (34) can be used to express Equation (35)
as:
( ) ( ) ( ) (
) (35)
For general model reference adaptive control, the adaptive
gains are commonly defined in a proportional plus integral
formulation
( ) ∫
(36)
( ) ∫
(37)
Where and are adaptive control weightings representing
the adaptive effort. is a scalar weighted function of the error
state and its derivatives, , where can be chosen
to ensure the stability of the feed forward block.
The equivalent scheme of MRAC for adjusting rotor currents
of DPC in this work is shown in fig. 8.
Fig. 8 The Simulink scheme of MRAC for rotor currents.
Fig. 9 The proposed DPC of a DFIG based on MRAC
VI. DISEIGN OF FLC CONTROLLER
The fuzzy controller used in this work has two inputs
and one output.
The fuzzy rule base consists of a collection of linguistic
rules of the form [4]
Rule 1: if is NB, and is NB then is NB.
Rule 2: if is NM, and is NB then is NB
Rule 3: if is NS, and is NG then is NS.
Rule 49: if is PB, and is PB then is PB.
These inferences can be made in a more explain as shown in
table.1 [4].
+-
+-
--
+-
+-
+-
irq
ird
Vrd
Vrq Ps
Qs
Rr +p*(Lr-Lm^2/Ls)
1
Rr +p*(Lr-Lm^2/Ls)
1
Ls*ωs
Vs^2
Lm*Vs g*
Lm*Vs
Ls -
Ls -
Lm*Vs
g*ωs*(Lr - (Lm^2/Ls))
g*ωs*(Lr - (Lm^2/Ls))
--
Pref
Qref
Adaptive
Controller
Vrq_ref
Vrd_ref
ird_meas
g*ωs*(Lr - (Lm^2/Ls))
g*ωs*(Lr - (Lm^2/Ls))
irq_meas
Lm*Vs
Ls -
Ls - Lm*Vs
g* Lm*Vs
Ls
Ls*ωs
Vs^2
Ps
Qs
Irq_ref
ird_ref Error
ird_ref
Error
irq_ref
+-
+-
--
--
--
+-
-- +
-
+-
+-
--
+-
+-
+-
ird_meas
irq_meas
Adaptive
Controller +-
PID
PID
Error
Irdq
Irdqref
Vrdq*
Kerror
1/S
1/S
α
β
G
G1
+
+
+
International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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TABLE.1. FUZZY INFERENCE TABLE.
NB NM NS EZ PS PM PB
NB NB NB NB NM NS NS EZ NM NB NM NM NM NS EZ PS
dS1,2 NS NB NM NS NS EZ PS PM
EZ NB NM NS EZ PS PM PM
PS NM NS EZ PS PS PM PB
PM NS EZ PS PM PM PM PB
PB EZ PS PS PM PB PB PB
The equivalent scheme of Fuzzy Logic control (FLC) for
adjusting rotor currents of DPC in this work is shown in figure
10.
Fig.10 The Simulink scheme fuzzy logic control for rotor currents.
Fig.11 The proposed DPC of a DFIG based on FLC
The overall system is described in detail, as shown in Fig.12.
Fig. 12 Global System.
VII. SIMULATION RESULTS
CASE I ( HYBRID MRAC-PID USING MPPT):
Fig. 13 Stator Active power Ps.
Fig. 14 Stator Reactive power QS.
Fig. 15 FFT analysis of spectrum THD of stator current is_abc (0.74%)
CASE II (HYBRID FLC-PID USING MPPT):
Fig. 16 Stator Active power Ps.
Fig. 17 Stator Reactive power QS.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-4000
-3000
-2000
-1000
0
1000
Ps meas MRAC (W).
Ps ref (W).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-1000
0
1000
2000
3000
4000
Qs meas MRAC (Vra).
Qs ref (Var).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-4000
-3000
-2000
-1000
0
1000
Ps meas FLC (W).
Ps ref (W).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-1000
0
1000
2000
3000
4000
Qs meas FLC (Var).
Qs ref Var).
Sta
tor
Acti
ve P
ow
er
PS_M
RA
C (W
).
Sta
tor
Acti
ve P
ow
er
PS_FLC
(W
).
Sta
tor
Reactiv
e P
ow
er
QS_M
RA
C (V
ar)
.
Sta
tor
Reactiv
e P
ow
er
QS_FLC
(V
ar)
.
Time (seconds).
Time (seconds).
Time (seconds).
Time (seconds).
Vdc
Doubly Fed
Induction
Generator (DFIG)
Park :
abc/dq
Rotor Side
Converter
(RSC)
3
2
Space Vector
Modulation
(SVM)
Direct Power
Control (DPC)
Park Inverse
dq/abc+
Concordia
abc/αβ
3
2 3
2
Bloc
3
Bloc
1 Bloc
2
Fig. (9-11) Fig.5 Fig.7
Pref
Qref
Vrq_ref
Vrq_ref
Irdq_meas
g*ωs*(Lr - (Lm^2/Ls))
g*ωs*(Lr - (Lm^2/Ls))
Irdq_meas
Lm*Vs
Ls -
Ls - Lm*Vs
g* Lm*Vs
Ls
Ls*ωs
Vs^2
Ps
Qs
Irdq_ref
Irdq_ref Error
Error
+-
+-
--
--
--
+-
-- +
-
+-
+-
--
+-
+-
+-
+-
PID
PID
Irdq
Vrdq* 1/G1
1/G
1/G Z
1
Unit Delay
Fuzzy Logic
Controller
Fuzzif
icatio
n
Intefe
rence
Defu
zzif
icatio
n
1
1
International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
5
Fig. 18 FFT analysis of spectrum THD of stator current is_abc (0.74%)
The DFIG used in this work is a 4 kW whose
nominal parameters are indicated in Table.2. And the wind
turbine used in this work is a 10kW whose parameters are
indicated in Table.3.
Fig.13 and Fig.16 present the stator active power and its
reference profiles injected into the grid using SVM for both
cases. It is clearly seen that the stator active power exactly
follows its reference to both cases; concerning the power error
is small using MRAC (Fig.13) for control of the rotor current
to the one using FLC (Fig.16). Fig.14 and Fig.17 show the
stator reactive power ant its reference using SVM for both
cases, we remark that the both reactive power equal to 0 Var,
that means the unity power factor. Using FLC-PID, we remark
the ripples in reactive power, is remarkable compared to
MRAC-PID, because the maximum of stator active power
equal to 4kW at 0.6sec, after that, the value of reactive power
becomes stable again equals to 0 Var.
Fig.15 and Fig.18 represent FFT analysis that helps us to
determine spectrum harmonics or the THD, which can
influence and disrupt the grid unless it has a low value. In our
work the THD of stator current using MRAC-PID and FLC-
PID equal to 0.74% (Fig.15 and Fig.18 respectively),
correspond in standard IEEE which should be lower than 5%.
VIII. APPENDIX
TABLE.2. PARAMETERS OF THE DFIG.
Rated Power: 4 Kwatts
Stator Resistance: Rs = 1.2Ω
Rotor Resistance: Rr = 1.8Ω
Stator Inductance: Ls = 0.1554 H.
Rotor Inductance: Lr = 0.1558 H.
Mutual Inductance: Lm = 0.15 H.
Rated Voltage: Vs = 220/380 V
Number of Pole pairs: P= 2
Rated Speed: N=1440 rpm
Friction Coefficient: fDFIG=0.00 N*m/sec
The moment of inertia J=0.2 kg*m^2
Slid: g=-0.04
TABLE.3. PARAMETERS OF THE TURBINE.
Rated Power: 10 Kwatts
Number of Pole pairs: P= 3
Blade diameter R= 3m
Gain: G=5.4
The moment of inertia Jt=0.00065 kg*m^2
Friction coefficient ft=0.017 N*m/sec
Air density: ρ=1.22 Kg/m^3
IX. CONCLUSION
In this work, two types of control have been proposed for
the control of the rotor current of the DFIG, using MRAC and
FLC respectively. The control of the DFIG should be more
robust because of the random shape of the winds. Using the
MPPT strategy for extracting maximum power and control of
the inverter is done via SVM. The results obtained using the
, have shown remarkable efficiency for
the both proposed methods, with a slight advantage of the
strategy MRAC compared with FLC, about the power error
and the THD of stator current injected to the grid.
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[2] S. Muller, M. Deicke, R.W. D. Doncker, “Doubly fed induction generator systems for wind turbines”, IEEE Industry Application Magazine, Vol.8, No.3, pp. 26-33.2002.
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International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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