Adaptive control for grid connected DFIG wind power generation system

Adaptive Control for Grid-Connected DFIG Wind
Power Generation System
Zhiguo Gao

Xiaohong Jiao

Chaobo Ge

Institute of Electrical Engineering
Yanshan University
Qinhuangdao 066004, China
Email:

Institute of Electrical Engineering
Yanshan University
Qinhuangdao 066004, China
Email:

Institute of Electrical Engineering
Yanshan University
Qinhuangdao 066004, China
Email:

the probability of requirements is that wind turbines should
remain connected and actively support to the grid during
disturbances. Accordingly, there has recently been a growing
interest in the context of the grid connected wind turbine with
DFIG, such as the dynamic responses[5], maximum power
control strategy[6], performance evaluation and control scheme
[7,8]
for the operation during abnormal conditions.

Motivated by the reason above, this paper provides a
control scheme for the grid connected wind turbine with DFIG
through back-to-back PWM. First, the overall model of a wind
power system is described, including the DFIG and a vectorcontrolled converter connected between the rotor and the grid.
Adaptive voltage controllers of the rotor-side and grid-side
converters are coordinately designed by utilizing nonlinear
adaptive control technology under consideration of the system
parameter uncertainty and grid disturbance, with the aim to
control the generation of wind power in order to maximize the
generated power with the lowest possible impact in the grid
voltage and frequency during normal operation and under the
occurrence of faults. Meanwhile, the comparative simulation
are presented between the proposed adaptive coordinated
controllers and PID controllers, showing that better dynamic
characteristics can be obtained using coordinated controllers.

Abstract—A novel control strategy is presented for the back-toback PWM converters of the grid-connected DFIG wind power
system to enhance the transient performance and reliability of
the overall system during physical parameter uncertainty and
certain grid disturbance. The system description is modeled by
using the field-oriented vector of the stator and voltage-oriented
vector of grid control. The rotor-side and grid-side converter
controllers are designed in integration by utilizing nonlinear
adaptive control technology. The theoretical analysis shows that
the proposed controller can guarantee the system to achieve the
maximal absorption of wind power, constant dc-bus voltage, and
constant voltage constant frequency output with respect to
variable wind-speed, parameter uncertainties and disturbance.
The effectiveness of the proposed strategy is validated by the
simulation comparison with the conventional PID controller.

Keywords-doubly fed induction generator; back-to-back PWM;
grid connection; wind power generation; adaptive control;
disturbance attenuation

I.

INTRODUCTION

As well known, DFIG is mainly used in variable speed
wind power systems due to its many advantages such as the
improved power quality, high-energy efficiency and reduced
power converter rating, etc. Consequently, in the decade, the
research of control problem for the grid-connected DFIG
through back-to-back PWM has received much attention as
one of preferred technology for wind power generation (see
[1-8] and the references therein).
Early research results mainly concentrated on the control
strategy for the rotor-connected converter of DFIG, which
applies the stator-flux-oriented vector technique to describe
model of DFIG, and then design PI controller[1,3] or robust
controller[2] to guarantee the wind power system to achieve the
maximal absorption of wind power and the decoupling control
for the active and reactive power of the generator. Before
connecting the stator of DFIG to the grid terminals, the stator
voltage has to be adjusted to be synchronized with the line
voltage. Thus, some references handle DFIG control for the
synchronization process, for example, [4] describes a smooth
and fast synchronization scheme of DFIG to the grid as well as
decoupling control of generator active and reactive power by
using the stator flux-oriented control at normal operation.

With increased penetration of wind power into electrical grids,

II.

SYSTEM DESCRIPTION AND CONTROL PROBLEM

The basic configuration of a grid-connected DFIM wind
power system is sketched in Fig. 1.
Rg

Lg u1a
Lg u1b

Rg

Lg u1c

Rg

udc

u2aL1 R1
u2bL1 R1
u2cL1 R1

Figure 1. Diagram of grid-connected DFIG wind power system

A. Overall model of the controlled system
For an induction generator, the stator field orientation
control is based on the stator d-q model, where the reference

frame rotates synchronously with respect to the stator flux,
with the d-axis of the reference frame instantaneously overlaps
the axis of the stator winding flux. The stator flux linkage
keeps constant when the system is in the steady-state operation

Project Supported by Natural Science Foundation of Hebei Province
(F2010001322)

___________________________________
978-1-4244-9690-7/11/$26.00 ©2011 IEEE



Te = n p Lm (isq ird − isd irq ) = Lm n pψ s irq / Ls

and the stator resistance is ignored. For such a reference frame
selection, the rotor voltage equations can be written as
dird
­
°u rd = Rr ird + σ dt − ω s 1σ irq
®
dirq
Lψ
+ ω s1 m s + ω s1σ ird
°u rq = Rr irq + σ
dt
Ls
¯

PM = 0.5 ρπ R 2C p (λ , β )v3 = kω (λ )ω 3

(1)

(2)

The active and reactive power can be respectively controlled
by controlling the q and d-axis rotor current. In addition, in the
case of ignoring the copper and iron loss of the stator, the
power relations for DFIG can be expressed as
P = Pe , P1 = sPe ± P1' , Pe =

Pm − Pm'
1− s

(3)

where Pe , Pm and Pm' represents electromagnetic power, input
mechanical power and the mechanical losses of the generator,
respectively. P1 and P1' denote the rotor power and rotor losses,
respectively. Furthermore, the power transfer relationship of
wind power generation systems is governed by
P=

ωs ( PM − PM' − Pm' )
n pωr

(4)

J©
Ls

¹
°
° L2ird = − R2ird + L2ω1irq + u1d + w2
° L2irq = − L2ω1ird − R2irq − ω1c1 + u1q + w3
®
°Cudc = 3 ( ed id − urd ird − urq irq + w4 )
2udc
°
° L1id = − R1id + ωs L1iq + ed − u2 d
° L1iq = − R1iq − ωs L1id + eq − u2 q
¯

where PM ; PM0 are the mechanical power captured by wind
turbine and mechanical wear of wind turbine, respectively.
Under the d-q reference frame, the equivalent circuit equations
of rotor side converter can be described as
­ dird
° Lg dt = − Rg ird + Lgωs1irq + u1d − urd
(5)
® dirq
° Lg
= − Lgωs1ird − Rg irq + u1q − urq
dt
¯
where
denote equivalent resistance and inductance,
are the output voltage of machine side converter in
the d-q axes. By combining (1) and (5), the integration model
of generator and rotor side converter can be obtained as
­

° L2
®
° L2
¯

dird
= − R2 ird + L2ω s1irq + u1d
dt
dirq
= − L2ω1ird − R2 irq − ω s1c1 + u1 q
dt

(9)

where v is wind speed, ρ is air density, λ =ω R / v is tip-speed
denotes power
ratio, R is the radius of wind turbine,
coefficient of wind turbine, is pitch angle.
In d-q coordinate, the circuit equation of grid side converter
can be described as
­ did
° L1 dt = − R1id + ω s L1iq + ed − u 2 d
(10)
® diq
° L1
= − R1iq − ω s L1id + eq − u 2 q
¯ dt
are the grid EMF components in d,q-axis,
where
are AC voltage and current in drespectively.

and q-axis components of the grid converter, respectively.
are the equivalent resistance and induction.
Ignoring the line loss and switching device switch loss,
according to energy conservation, grid side input power equals
to stored power of the DC side capacitance and excitation
power of the rotor side, therefore:
du
3
Cudc dc = ( ed id + eqiq − urd ird − urqirq )
(11)
dt
2
Conservation of energy for converter side:
95
du
ed id = cudc dc + P2
(12)
dt
100
Considering external disturbance and (6), (7), (10) and (11),
we can get the overall model of DFIG wind power system:
­
·
1§
nLmψ sωs
2
irq − Bω + w1 ¸
°ω = ¨ kωω −

where

represent rotor voltage and currents in
is rotor resistance.
d-q axis reference frame, respectively.
is leakage factor, , , represent rotor, stator
inductance and mutual inductance, respectively.
is slip frequency, , represent synchronous angular speed
is the number of pole pairs.
and rotor speed, respectively.
The stator active and reactive power can be described as
Lmψ s ω s
­
irq
°° P = u sd isd + u sq isq = − L
®
ψs s − Lm ird
°Q = u sq isd − u sd isq = ω sψ s
Ls
°¯

(8)

The power PM produced by the wind is given by

(13)

where n = n p ng , wi (i = 1," , 4) denote external disturbances.
B. Control problem formulation
Generally, for the wind power system (13), the main goals
of the control strategies are:
(1) Maximize the produced energy in the assurance of a

secure functioning of the turbine;
(2) Control the active power supplied by the turbine in
order to optimize the operating point and limit the active
power in case of high wind speed;
(3) Control the reactive power flow between the generator
and the grid, especially in the case of weak grids, where
voltage fluctuations can occur, to guarantee the quality of the
grid voltage.
Moreover, it should be noted that during system operation
there exist uncertainties, including parameters uncertainty and
external disturbance, such as, physical variables B and
are
of susceptible. Thus, let
,
,
be unknown parameters. Therefore, the task in this paper is to

(6)

where c1 = Lmψ s / Ls , R2 = Rr + Rg , L2 =σ + Lg .
The motion equation of wind turbine with DFIG is described as
P
dω
(7)
J
+ Bω = M − n g Te
dt
ω
where
,

.
denote the
moment of inertia, viscous friction coefficient of wind turbine
and generator, respectively. Te denotes electromagnetic torque
generated, which can be calculated by




design the global controllers for the rotor-side and grid-side
converters to ensure the wind power system (13) to achieve
the above control objective regardless of uncertain parameters
and external disturbance
during normal operation and under the occurrence of faults.
To this end, define:

ν

isd

isq

ω

ird
irq

udc
u1q

u1d

id

u2d

θˆ

u2q

iq

θˆ

x1 = ω − ω , x2 = ird − i , x3 = irq − i , x4 = udc − u , x5 = id − i , x6 = iq − i
∗

∗
rd

∗
rq

∗
dc

∗
d

∗

q

then (16) can be rewritten as

Figure 2. Block diagram of the grid connected wind power control system

1
­
∗
°x1 = J ( f1 ( x1 , kω ,ω ) −θ1 x3 −θ2 x1 + w1 )
°
1
f2 ( x2 , x3 , irq∗ ,ω∗ ) + u1 + w2
°x2 =
L
2
°
1
°x3 =
f3 ( x2 , x3 , ird∗ ,ω∗ ) + nx1θ3 + u2 + w3
L2
°°
ª
®
Lr
Lr
∗
∗
∗
∗

°x4 = d « Ex5 + f4 ( x2 , x3 ,ird ,ω ) + ( x2 + ird ) w2 + ng x1irqθ3
L
L
2
2
¬
°
º
L
L
°
− r (ωs − ng x1 − ngω∗ ) x3θ3 + r ( x3 + irq∗ ) w3 + w4 »
°
L2
L2
¼
°
R
R
°x5 = − 1 x5 + ωs x6 − u3 , x6 = − 1 x6 − ωs x5 − u4
L1
L1
°¯

(
(

)

)

III. ADAPTIVE COORDINATED CONTROLLER DESIGN
In this section, an adaptive controller based on coordination
will be designed for system (14) by utilizing the nonlinear
recursive technique. First, to design controller, the following
coordinate transformation is utilized for the system

(14)

∗
ξ 4 = ( x4 + udc
) + d1 ( x2 + ird∗ ) + d1 ( x3 + irq∗ ) − d1udc∗ − d1ird∗ − d1irq∗
2

(

+ R −

u1 = u1 d − L r
u 2 = u1 q − L r

∗
d ird
dt
∗
dirq

dt

∗

rd

2
2

2
3

2

∗
rq 3

Lr
L2

∗
rd

2

Lr
L2

3

∗
2 1d

Lr

L2

1

∗
rq

2

Lr
L2

2

2

(15)

where
Thus, we get the following conclusion.
Proposition1: For system (14), if a coordinated controller for
the rotor-side converter and grid-side converter is designed as:

)( x + 2i x ) + ( x + i ) v + x u
)( x + 2i x ) + ( x + i ) v + x u

R2 Lr
L2
R2 σ
r

L2

2

ξ 4 = d ( Ex5 + f 4 + I1 x2 w2 + c2θ 3 + I1 x3 w3 + w4 )

fi = − R2 xi ± L2ω s x j B L2 n ( x1 + ω ∗ ) x j B L2 nirq∗ x1 , i , j = 2,3(i ≠ j )

(

2

Then, it follows˖

with d1 = 3/(2C ) , f1 = kω x12 + 2kωω ∗ x1 ,
f 4 ( x2 , x3 , ird∗ ,ω ∗ ) = Rr −

2

2x2
R1
­
°u1 =− f2 − L γ 2 − L2k2 x2 , u4 =− L x6 −ωs x5 + k6 x6
1
2
°
ˆ
ª
°u = L «−k z + x − f3 − 2z3 − 2 (∂α1 )2 z − nx1θ3
° 2 2 ¬ 3 3 1 L2 L2γ 2 J 2γ 2 ∂x1 3 L2

°
∂α
∂α º
1 ∂α1 ˆ
θ x +θˆ x + 1 ω∗ + 1τˆ»
+
°
∂τˆ ¼
J ∂x1 1 3 2 1 ∂ω∗
°
2
1
1 ∂α2
1 § ∂α2 ·
R1
°
(16)
®u3 =− L x5 +ωs x6 + E {ξ4 + J ∂x f1 −θˆ1x3 −θˆ2 x1 + 2 2 ¨ ∂x ¸ z4
Jγ © 1¹
1
1
°
∂α
1 ∂α2
1 ∂α2
° +
f + nx1θˆ3 + u2 + 2 (Ex5 + f4 + c2θˆ3 )
( f +u ) +
L2 ∂x2 2 1 L2 ∂x3 3
∂ξ4

°
2
2
1 § 1 ∂α2
∂α2 ·
∂α2 ˆ ∂α2 ∗ ∂α2 ∗ 1 § ∂α2 ·
°
° + γ 2 ¨ L ∂x + I1x2 ∂ξ ¸ z4 + ˆ θ3 + ∂i∗ irq + ∂i∗ irq + γ 2 ¨ ∂x ¸ z4
∂θ3
© 2 2
© 4¹
4¹
rq
rq
°
2
° + ∂α2 u∗ + ∂α2 u∗ + 1 § 1 ∂α2 + I x ∂α2 · z + k z }
1q
∗ 1d
°
γ 2 ¨© L2 ∂x3 1 3 ∂ξ4 ¸¹ 4 5 4
∂u1∗q
¯ ∂u1d

∗
3 1q

1 ª
di ∗
u 2 d − ( L1 dtd − R1id∗ + ω s L1iq∗ ) º ,

¼
L1 ¬
1 ª
diq∗
∗
∗
∗
∗
∗ º
u 2 q − ( L1 dt − R1iq + ω s L1id )
+ R r irq − L r ω 1ird + u rq , u 4 =
¼»
L ¬«

∗
∗
∗
, u3 =
+ R r ird
− L r ω 1irq
+ u rd

(

1

∗
, id∗ , iq∗ are the reference values of the wind
where ω ∗ , ird∗ , irq∗ , udc
turbine speed, current d-q components of generator rotor, DC

voltage and current d-q components of grid-side, respectively,
which can be obtained by the following relationship.
To electively extract wind power while at the same time
maintaining safe operation, the wind turbine should be driven
according to the three fundamental modes associated with
wind speed, maximum allowable rotor speed and rated
power[9]. Consequently, the desired wind turbine speed ω ∗ and
the expected captured wind power PM∗ are given. According to
the requirement for reactive power, the expected reactive
power Q∗ can be known. Further, by (2), (4) and (12), ,
and can be obtained. To achieve the control of unity power
factor of converter, the value of is 0.
Therefore, the control problem of this paper is to design an
adaptive controller
for the system (14)
where, is an estimate for the unknown parameter , which
makes the resulting closed-loop system operate safely and
stably and achieve the control goal in the presence of the
parameter perturbation and external disturbance, i.e. the speed
of wind turbine achieves asymptotically tracking the desired
speed trajectory based on the maximum capture of wind
energy. Simultaneously, the voltage of DC side is constant
and the grid-side converter exports electrical energy of
constant voltage and constant frequency in the required power
factor. The diagram of integrated control system of wind
power generation system is shown in Fig. 2.

)

(

(

)

)

and the adaptive update law is chosen as follows˖
z ∂α
z ∂α2
z ∂α1
­ ˆ z4 ∂α2
x3 − 3 1 x3 ,θˆ2 = 4
x1 − 3
x1
°θ1 =

r1J ∂x1
r1J ∂x1
r2 J ∂x1
r2 J ∂x1
°
®
§
·
§
·
∂
α
∂

α
c
1
2
2
2
°θˆ3 = − ¨ ξ4 +
z4 ¸ −
nx1 ¨ z3 +
z4 ¸ ,τˆ = Γ1−1ψ1T ( x1 )
r3 ©
∂ξ4 ¹ r3L2 ©
∂x3 ¹
°¯

(17)

where ψ1(x1) = ª¬ f1x1 − x12 2x12 γ 2 º¼ , k2,k3,k6 >0 are tuning parametersˈ
α1 , α 2 are the virtual control inputs determined in the proofˈ
Γ1 = diag{r4 , r5 , r6} ˈ ri > 0, (i = 1," 6) ˈThen the resulting closedloop system has the following operation performance:
(1) when w = 0 ˈ the system is Lyapunov stable at the
equilibrium and states x can converge to the origin, namely,
ω → ω ∗ , ird → ird∗ , irq → irq∗ , udc → udc∗ , id → id∗ , iq → iq∗ as t → +∞ .
(2) when w ≠ 0 , the system from the disturbance input w to
the penalty output signal y = [ ρ1x1 ρ 2 x2 ρ3 z3 ρ 4ξ 4 ρ5 z5 ρ6 x6 ]Τ )
has -gain not large than γ , ρi are weighted coefficients.
Outline of Proof: The controller (16) and the adaptive update
law (17) are derived by nonlinear adaptive backstepping
design technique, where Lyapunov function of the closed-loop




system is recursively constructed. The proposition is obtained
according to Lyapunov stability theorem and LaSalle invariant
principle as well as L2-gain disturbance attenuation technique.

impact in the grid voltage and frequency during normal
operation and under the occurrence of faults with parameter
uncertainties and external disturbance, such as in case 1 and
case 2.

IV. SIMULATION VALIDATION
The effectiveness of the designed controller is validated by
simulation in MATLAB/SIMULINK and the comparison with
that of PID controller is given.
A simulated wind speed and the corresponding desired
speed of wind turbine are shown in Fig. 3
w*

1.96

*

1.94

14
1.92

80

100

120

The following two operation cases are discussed The fault
considered in simulations is a symmetrical three phase short
circuit fault which occurs on one of the transmission lines.
(1) Uncertain parameters and external disturbance: In the
operation the physical variables B and
contain uncertainties
and there exists external disturbance .
(2) The occurrence of faults: The system is in a pre-fault
operation state, a symmetrical three phase fault of grid voltage
occurs at t=80s.
The simulation results in case1 are shown in Fig.4 and Fig.5.
To compare the control performance, the curve is also given
for the system under the action of PID controller. The
simulation results in case2 are shown in Fig 6.
2

60
t/s

90

rq

i •A
•

rd

i •A
•

i

50
t/s

w
(m
/s)

i •A
•

i • A•

[1]

*

iq
iq

q

i • A•

[3]

PID

0

*

id
id

-5
0

PID

100

50

t/s

[4]

100
t/s

Figure 4. The response curves of the closed-loop system in case 1
0

v1
v2

v3
v4

[5]

-200
v3,v4• V•

v1,v2• V•

1000

0

-1000

-2000
0

-400

-600

[6]
20

40

60

80

100

-800
0

120

20

40

t/s

60

80

100

120

t/s

50

70
1

60

2

0
, ,

30
20

1 2 3

3

40

, ,

1 2 3

50

[7]

-50
1

-100

2

10
0
0

20

40

60
t/s

80

100

120

80

100

120

i*

i*

q

PID

d

PID

50

100

-5
0

50

100
t/s

Figure 6. The response curves of the closed-loop system in case 2

100

5

2000

60
t/s

0

t/s

rq

10

d

i • A•

-4
0

[2]

0
0

0

50

40

5

-2
-3

PID

-1

-4
0

20

i

-1

i*
rq

t/s

-3

0
0

10

q

0.1

100

-2

100

0

0.05
50

PID

0.06
0.04

50
t/s

100

0.2

5
0
0

PID

REFERENCES
50
t/s

0.15

PID

Irq

0.08

0.02

0
0

dc

349.4
0

rd

10

i*rq

0.1

i rd

10

100

0.12

*
i rd

5

u

rd

i

PID

50
t/s

349.8

i*

15

dc

u

347
0

100

15

350

120

20

u*

348

50

20

349.6

30

349

t/s

PID

1.9
1.85
0

350

dc

1.85
0

u*

350.2

1.95

1.95
1.9

dc

u•V

•

w• m
/s•

2.05

351

w*
w
PID

2

id

350.4

w*
w
PID

d
c

2.1

2.1
2.05

u•V
•

60
t/s

rq

40

i • A•

20

Figure 3. Wind speed and the desired speed ω ∗ of the wind turbine

q

1.9
0

100
t/s

i• A
•

50

rd

12
0

d

16

w(m
/s)

v(ra
d
/s)

1.98

d
c

2

v

18

V. CONCLUSION
In this paper, the adaptive coordinated control of rotor-side
converter and grid-side converter is investigated via the vector

control strategy. The theoretical analysis shows the designed
controller can guarantee the system on grid operation has good
dynamic performance irrespective of uncertain parameters and
external disturbance. The simulation results also illustrate that
the proposed control scheme can achieve the maximal
absorption of the wind power according to three wind turbine
operation modes, control the active power supplied by the
turbine to optimize the operating point, control the reactive
power flow between the generator and the grid to guarantee
the quality of the grid voltage.

-150
0

3

20

40

60
t/s

80

100

[8]

120

Figure 5. Control inputs and estimates of adaptive parameters

From the simulation results, it can be concluded that:
The nonlinear adaptive coordinated controller
proposed in this paper can effectively improve transient
stability of the system and achieve the control aim
maximizing the generated power with the lowest possible

[9]



R. Pena, J.C. Clare, G.M. Asher, "Doubly fed Induction generator using
back-to-back PWM converters and its application to variable-speed
wind-energy generation". IEE Proc.-Electric Power Application,vol. 143,
no. 3, pp. 231-241, May 1996..
S. Peresada, A. Tilli, A.Tonielli. "Robust active-reactive power control
of a doubly-fed induction generator". Proceedings of the 24th Annual
Conference of the IEEE, 1998.
A. Tapia, G. Tapia, J. X. Ostolaza, and J. R. Saenz, “Modeling and
control of a wind turbine driven doubly-fed induction generator,” IEEE
Trans. Energy Conv., vol. 18, no. 2, pp. 149–204, June 2003.
A.G Khalil, D.C. Lee, S.H. Lee. "Grid connection of doubly-fed
induction generators in wind energy conversion system". IEEE 5th
International Power Electronics And Motion Control Conference, 2006.
A. Perdana, O. Carlson, J. Persson."Dynamic response of grid-connected
wind turbine with doubly fed induction generator during disturbances".
Nordic Workshop on Power and Industrial Electronics. Trondheim, 2004
M. B. Bana sharifian, Y. Mohamadrezapour, et. al. "Maximum power

control of grid connected variable speed wind system through back to
back converters". J. Applied Science, vol. 23, no.8, pp. 4416-4421, 2008
Y. Lei, A. Mullane,et. al. "Modeling of the wind turbine with a doubly
fed induction generator for grid integration studies". IEEE Trans. Energy
conversion, vol. 21, no. 1, pp. 257-264, 2006
J. Hu,Y. He. "Modeling and enhanced control of DFIG under unbalanced grid voltage conditions". Electric Power Systems Research, vol. 79,
pp. 273–281, 2009
Y.D. Song, B. Dhinakaran, X.Y. Bao, "Variable speed control of wind
turbines using nonlinear and adaptive algorithms". Journal of Wind
Engineering and Industrial Aerodynamics, vol.85, pp.293-308, 2000.