Modeling and Power Controls of Wind Energy
Conversion Systems Based on Doubly Fed Induction
Generator
Manale Bouderbala*, Badre Ahmed Lagrioui Mohmmed Taoussi, Madiha El Ghamrasni
Bossoufi, Hala Alami Aroussi Department of Electrical Yasmine Ihedrane Mohammadia School of
Laboratory of Electrical and Computer LISTA Laboratory Engineers
Engineering and Maintenance Engineering The Higher Faculty of Sciences Dhar Elecrtrical 'epartment
Higher School of Technology National School of Arts El Mahraz, University 5DEDW0RURFFR
Oujda, Morocco and Trades, Sidi Mohammed Ben
*Bouderbala.manale@gPDLOFRP Moulay Ismail University Abdellah
Meknes, Morocco Fez – Morocco
Abstract—. This study focuses on the wind energy conversion achieve this, the system control is necessary to make the most
systems which consist of a turbine, multiplier, generator and of available resources. [3]
power electronic devices. In our case we opted for the doubly fed In this work, we will present the modeling of WECS which
induction generator (DFIG); this choice is due to its advantages is based on DFIG. From this latter, we can exploit the wind
as well as its ability to adapt to changing wind. On the other resources for different wind conditions since it allows the
hand, this machine is characterized with its non-linearity. production of energy at variable speed. After that, we will pass
Moreover, it is necessary to apply a control in order to have a through to the control of the system which is the most critical
maximum of power and to maintain the reactive power at zero. phase; starting with the optimization of the energy conversion
Therefore, we will start with the modeling of the system. Then,
and ending with the control of the active and reactive powers.
the maximization of the power using the strategy of maximum
power point tracking (MPPT) will be detailed, finally, we will
In order to be able to achieve this, we will use the MPPT
apply the two control techniques namely: direct field oriented control strategy and the direct and the indirect field oriented
control (DFOC) and indirect field oriented control (IFOC) in controls, then we will compare between the two techniques
order to compare them. The results are presented in the Matlab/ based on the simulation results that will be presented in the
Simulink environment to ensure the performance of the control. Matlab/Simulink environment.
Keywords-component; Wind Energy Converion System II. MODELLING OF A
(WECS), Doubly- fed induction generator (DFIG), Direct field WIND ENERGY CONVERSION SYSTEM
oriented control (DFOC), Indirect field oriented control (IFOC), The Wind Energy Conversion System is illustrated as
MPPT strategy. follows fig.1. It consists of a turbine which ensures the
conversion of kinetic energy into mechanical energy. Then, the
I. INTRODUCTION multiplier has the role of adapting the speed of the turbine with
To deal with the current and increasing demand of energy, the speed of the generator. Finally, the DFIG converts the
it is necessary to find inexhaustible sources: among these mechanical energy into electrical energy where; the stator is
resources called "renewable energies", we have the wind directly connected to the grid unlike the rotor which is
energy that presents an important potential. Also we can not connected via the power electronic devices. [4] [5]
deny the interest of research centers today towards renewable
energies. Thus, the development of wind turbines represents a
major investment in the technological search and that is why
wind farms are ubiquitous today. [1][2]
Many of these wind farms are based on the Doubly Fed
Induction Generator (DFIG) technology with converter ratings
around 30 percent of the generator ratings. However, to make a
cost-effective wind energy conversion system, it must be able
to extract as much of the available energy as possible. To
Figure 1. : Wind Energy Conversion system
The equations below describe the system to be studied: C. Doubly Fed Induction Generator
The mathematical model of DFIG in the park referential (d-
A. Wind turbine q) is given by the following equations: [9] [10]
The aerodynamic power (Paer), which is converted by a Electrical equations:
wind turbine, depends on the wind power as well as the power
coefficient (Cp) which is determined according to Betz's law
and is expressed as a function of the relative speed λ
representing by [6] d ) sd
Vsd Rs .I sd ) sq .Zs
dt
Paer Cp(O , E ).Pv V d ) sq
sq Rs .I sq ) sd .Zs
dt
The wind power and the ratio λ are determined as follows:
d ) rd
[6] [7] Vrd Rr .I rd ) rq .Zr
dt
U .S .V 3 d ) rq
Pv Vrq Rr .I rq ) rd .Zr
2 dt
The frequency of the stator voltages is imposed by the grid
but the pulsation of the rotor currents is given by: [11]
R.:t
O
V Zr Zs Z
ρ : density of the air which equal to 1,225 Kg \ m3
S: area swept by the pales of the turbine (π .R²) Z p.:
V: wind speed.
The flux equations: [12]
Ωt: speed of the turbine.
R: wind turbine radius.
) sd Ls .I sd M .I rd
B. The multiplier
) sq Ls .I sq M .I rq
Ct ) rd Lr .I rd M .I sd
Cg
G ) rq Lr .I rq M .I sq
The electromagnetic torque as a function of the stator field and
:mec rotor currents is given by: [13] [14]
:t
G M
Cem p. .() sq .I rd ) sd .I rq )
Ls
Cg: generator torque.
Ωmec: mechanical speed of the generator (11)
G: multiplier gain Vs (d,q), Vr (d,q): stator and rotor voltages in the reference of
PARK.
The following relationship describes the aerodynamic
φs (d, q), φr (d, q): stator and rotor flux in the reference of
torque: [7]
PARK.
d :mec Is (d, q), Ir (d, q) stator and rotor currents in the reference of
J Cmec Cg Cem C f .:mec (6) PARK.
dt Rs, Rr: stator and rotor resistances.
Cem: electromagnetic torque. Ls, Lr: cyclic stator and rotor Inductances.
Cmec: mechanical torque M: mutual inductance.
p: Number of pole pairs of the machine.
Cf: viscous friction torque
ωs: Pulse of the stator electrical quantities.
J: total inertia ωr: Pulse of the rotor electrical quantities.
III. MAXIMIZATION OF THE POWER OF THE WIND In order to simplify the control, we will orient the flux
CONVERSION SYSTEM along the axis d (fig.3) [15] [16] [17]
The MPPT control is used to extract the maximum power;
it is based on adjusting the speed of the turbine which allows to
extract the maximum of power.
From the equation (1) we can conclude that the
aerodynamic power depends (Paer) on Cp and wind power.
Indeed, for each wind speed V, the power - rotation speed
characteristic goes through a maximum corresponding to a
maximum power reached for an optimal rotation speed.
However, the maximum power is obtained for a maximum
power coefficient, this later corresponds to an optimum specific Figure 3. Orientation of the stator flux on the axis d
speed and this specific speed is obtained for an optimum
With:
rotational speed (fig.2) [2] [7]
The expression of the reference power becomes:
) sd ) s and ) sq 0 (15)
For high power machines, the stator resistance is
Paer _ ref Cp(O , E ).Pv _ est neglected and it is also assumed that the flux is constant so we
can write: [17]
The estimated value of the wind speed: Vsd 0
(16)
Vsq Vs ) s .Zs
R.:t
Vest From equations (10) (15) we can write:
(11)
Oopt
The expression of the reference electromagnetic torque
) sd )s Ls .I sd M .I rd
(17)
which must be applied to the DFIG is: ) sq 0 Ls .I sq M .I rq
Paer ref The equations connecting the stator currents with the rotor
Cem _ ref currents are written as follows by:
:t
)s M
I sd .I rd
Ls Ls
(18)
M
I sq .I rq
Ls
By replacing flux and stator currents in the equation (10),
by the expression (18), we obtain:
M2 Vs.M
) rd ( Lr ).I rd
Ls Ls .Zs
M²
) rq ( Lr ).I rq
Ls
Figure 2. MPPT Strategy control
IV. FIELD ORIENTED CONTROL By replacing the expressions of the equation (19) in the
equation(7), we have:
Referring to equation (11), we can see the strong coupling
between the rotor and stator flux and currents which makes the
control of the DFIG more difficult.
To work out with this, we propose to direct the flux vector to
make this machine similar control standpoint to a DC machine.
M 2 dI rd M2
Vrd Rr .I rd ( Lr ). g.Zs .( Lr ).I qr The figure below represents the aerodynamic power,
Ls dt Ls and the fig.6 represents the Cp coefficient .
M 2 dI rq M2 M .Vs
Vrq Rr .I rq ( Lr ). g.Zs .( Lr ).I dr g. 6
Ls dt Ls Ls x 10
1.5
(20) (28)
1
The powers expressions become:
0.5
Paer
Vs .M
Ps .I rq 0
Ls
(21) -0.5
Vs 2 V .M
Qs s .I rd
Ls .Zs Ls -1
0 2 4 6 8 10 12 14 16 18 20
times(s)
According to the last equation, we conclude, that the stator
active power depends on the quadrature rotor current and the Figure 5. aerodynamic Power
reactive power depends on the direct rotor current.
To control these powers, we define two methods of Field
Oriented Control: 0.6
A. Direct Field Oriented Control (DFOC)
0.4
This method acts directly on the voltages by applying a PI
regulator on each axis and neglecting the coupling terms
between the two axes. [15] [16] Cp 0.2
B. Indirect Field Oriented Control (IFOC) 0
This method consists in putting 2 regulators at the level of
-0.2
each axis one to regulate the power and another for the current,
considering the coupling terms. [15] [16]
-0.4
V. SIMULATION AND INTERPRETATION RESULTS 0 2 4 6 8 10 12 14 16 18 20
In order to test our control, we will apply a wind profile times(s)
Fig.7 which consists of harmonic sums corresponding to the
pulse ω. It is modeled by the following equation: Figure 6. Cp Coefficient
n
V V0 ¦ Ai .sin(Zi t )i )
i 1 From the fig.4 and the fig.5 we can note that the
aerodynamic power corresponds perfectly to the wind speed.
10.5
From fig.6 we can easily deduce that with the MPPT
10
strategy we can have a power coefficient equal to 0.5 which is
9.5 the maximum value to extract the maximum power.
The figures below represent the DFOC and IFOC
wind speed (m/s)
8.5
simulations:
7.5
6.5
0 2 4 6 8 10 12 14 16 18 20
times(s)
Figure 4. Wind speed
6 6
x 10 x 10
0 0
Ps-mes Ps-mes
Ps-ref Ps-ref
-0.5 -0.5
-1 -1
P(W)
P(W)
-1.5 -1.5
-2 -2
-2.5 -2.5
-3 -3
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
times(s)
times(s)
4 4
x 10
x 10 12
12 Qs-mes
Qs-mes 10 Qs-ref
10 Qs-ref
8
8
6
Qs (Var)
Qs (Var)
4
4
2
2
0
0
-2
-2
0 2 4 6 8 10 12 14 16 18 20 -4
0 2 4 6 8 10 12 14 16 18 20
times(s) times(s)
0
0
-500
-500
-1000
-1000
-1500
-1500
-2000
Irq (A)
-2000
Irq (A)
-2500
-2500
-3000
-3000
-3500
-3500
-4000
-4000
-4500
0 2 4 6 8 10 12 14 16 18 20
times(s) -4500
0 2 4 6 8 10 12 14 16 18 20
times(s)
200
250
150
200
Ird (A)
100 150
Ird (A)
100
50
50
0
0 2 4 6 8 10 12 14 16 18 20
times(s) 0
0 2 4 6 8 10 12 14 16 18 20
Figure 7. DFOC simulations times(s)
Figure 8. IFOC simulations
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