Energy and Power Engineering, 2013, 5, 377-381
doi:10.4236/epe.2013.54B073 Published Online July 2013 (http://www.scirp.org/journal/epe)
LVRT Research of PMSG Wind Turbine Using
Feedback Linearization
Jie Wei1, Zhenyu Lin2, Nian Liu1
1Smart Grid Key Laboratory of Sichuan Province, School of Electrical Engineering and Information,
Sichuan University,Chengdu, China
2College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China
Email: vajay4920@sina.com
Received February, 2013
ABSTRACT
Analyzing the wind turbine with a direct-driven PMSG, this paper proposes a low voltage ride through scheme of
PMSG wind power systems based on feedback linearization. The DC-Link voltage is controlled by the generator-side
converter rather than the grid-side converter. Considering the nonlinear relationship between the DC-Link voltage and
the generator rotor speed, the controller of DC-Link voltage uses a feedback linearization technology. The grid-side
converter which controls the grid active power according to the maximum power point tracking adds a judgment link
for the generator speed reference. The model of 2 MW PMSG wind power system was simulated by using PSCAD. The
simulation result has verified the validity of the proposed control scheme.
Keywords: PMSG; DC-Link Voltage; Converter; PSCAD
1. Introduction
Among various renewable energy sources, the applica-
tion of wind power generation in the world has been rap-
idly growing. Unlike the DFIG (double fed induction
generator) wind power system, direct-drive PMSG (per-
manent magnet synchronous) wind power system have
some advantages such as simple structure, high power
generation efficiency, high precision and high operating
reliability[1].
Because of the growing proportion of the wind field,
the grid-connected conditions of wind power generator
are more and more important. In recent years, many
countries in the world have promulgated special inter-
connection rules and processes for large-scale wind
power units through a grid code [2,3].
Scholars at home and abroad have proposed a large
number of schemes for the LVRT (low voltage ride
through) capability of the DFIG wind turbines [4-7],but
researches on direct-drive PMSG is very limited. Refer-
ence [8] increased the speed of the generator and reduced
the converter input power in order to realize the LVRT,
but the improving level is very limited and the DC-Link
voltage may exceed the limit. In [9] and [10], Crowbar
circuit absorbed the unbalanced power in the power grid
fault, however, in this way, the unbalanced power would
be completely waste, which needing the support of load
and heat dissipation. The STATCOM can be used to
supply the reactive power compensation for wind power
turbines in the power grid fault [11], however, when the
fault occurs and ends, the cut-in and cut-out of the
STATCOM make the control more complex, and in-
vestment cost is also great.
For PMSG wind power system with back-to-back
PWM converters, in the conventional control method
[12], the generator rotor speed is controlled by the gen-
erator- side converter, and the grid-side converter control
the DC-Link voltage. Considering the nonlinear rela-
tionship between the DC-Link voltage and the generator
rotor speed, this paper proposes an improved control
method of the power conversion. The DC-Link voltage is
maintained within regular range by the generator-side
converter which introduces feedback linearization control
technology. The generator speed reference ω* is output
by the grid-side converter for the maximum power point
tracking, and the ultimate value ωw* is got after com-
parative judgment with ω*.
2. Mathematical Model of PMSG
Wind Power Sysrem
According to the aerodynamicsthe simplified mathe-
matical model of wind turbine is formulated as[13]:
23
1(, )
2
/
wp
w
PRvC
Rv


(1)
*The project sponsored by Science and Technology Department o
f
Sichuan Province(2011GZ0036).
Copyright © 2013 SciRes. EPE
J. WEI ET AL.
378
where Pw is the extracted wind power, ρ the air density, v
the wind speed, R the rotor radius, ωw the wind turbine
speed, Cp the efficiency coefficient.
In the synchronous d-q coordinates, the mathematical
model of PMSG are[14]:
sd
sds sddqsq
sq
sqssqqdsd
di
uRiL Li
dt
di
uRiL Li
dt

 
 
(2)
where usd and usq are the d-q stator voltage, isq and isq the
d-q stator currents, Rs and Ls are stator resistance and
inductance, ω the generator speed,
magnet flux.
Using the control strategy of , the generator
electromagnetic torque is:
0
d
i
3
2
en
Tpi
sq
(3)
where is the number of pole pairs.
n
Neglecting the loss of converter and generator, the
generator power and the DC-Link capacitor C are:
p
w
gw w
d
PPJdt
 (4)
dc
cdc ggri
du
PuC PP
dt

d
(5)
where Pg is the generator power, udc the DC-Link voltage,
Pgrid the gird power.
Combining Equations (4) and (5), a dynamic equation
can be introduced:
53
3
11
2
dc w
dcp wwgrid
du d
uCRCJP
dt dt
 
 (6)
In the above Equation (6), the nonlinear relationship
between udc and ωw can be shown.
3. Control Strategy
3.1. Control Scheme of the Grid-side PWM
Converter
When the wind turbine power P is less than the rated
power, the rotor speed reference ωw* can be expressed as
follows by P[15]:
*2
0.671.42 0.51
wPP
 (7)
According to Equation (7) for the MPPT, the rotor
speed reference ωw* can be got.
As shown in Figure 1, when the rotor speed is greater
than 1p.u, ωw* is set to 1 in order to make the generation
system can according to the active power demand of the
gird-side ensure that the generator rotor work in the best
reference.
The control block diagram of the grid-side PWM con-
verter is shown in Figure 2.
*
w
*
1?
w
*
1
*
1
w
Figure 1.Control block diagram of the grid-side PWM con-
verter.
*
11?
Figure 2.Control block diagram of the grid-side PWM con-
verter.
3.2. Control Scheme of the Generator-side
PWM Converter
The state equations of a single input and single output
system can be represented as follows:
() ()
()
x
fx gxu
yhx

(8)
Where x is the state vector, u the control input, y the
output, h the smooth scalar function, f and g are the n
dimensional smooth vector field.
The nonlinear Equations (4) (5) can be written in the
state equations as follows:
11
11
grid
dc dcdc
g
ww
ww
P
uuC uC
P
P
JJ

 

 

 


 


 
 
(9)
For the system design methodology, the DC-Link vol-
tage is used as the control input. In order to realize the
linear process, the output y is for the difference.
()()()
fg
yhfguLhxLhx
u
  (10)
where is the first order Lie derivatives of h(x)
along f, along g. Here, the first order Lie de-
rivatives is defined as follows:
()
f
Lhx
(
g
Lhx)
f
g
h
Lh hff
x
g
Lh hgf
x
 
 
(11)
Copyright © 2013 SciRes. EPE
J. WEI ET AL.
Copyright © 2013 SciRes. EPE
379
Without loss of generalityEquation (12) is given as: paper simulates 2 MW PMSG wind power system based
on PSCAD. Imitating the grid connection point voltage
drops to 50% in 1 s -1.5 s, the proposed new method is
compared with the conventional method in this paper.
The system parameters are as follow.
() ()
()()
g
f
Lhx Ax
Lhx Bx
(12)
Hence, Equation (13) can be derived from Equations
(10) and (12). PMSG: Stator rated voltage 690 V, Magnetic induc-
tion 1p.u, Stator phase resistance 0.008 p.u, Direct-
axis inductance Xd 0.062 p.u
Quadrature axis in-
ductance Xq 1.1477 p.u.
() ()yBx Axu
 (13)
Combining Equations (9) and (13), Equation (14) is
represented as follows: Wind Turbine: Air density 1.225 kg/m3, Rated wind
speed 10m/s.
1
()
1
()
g
rid
dc
dc
A
xP
uC
Bx uC

(14)
Converter: DC-Link voltage 1100V, Rated output
voltage 690 V, Reactive power setting value 0 Mvar,
Grid frequency 50 Hz.
The grid output power is minished along with the grid
connection point voltage drops to 50%, which, at the
same time, causing the generator output power reduction.
The unbalanced power between the grid-side and the
generator-side will cause DC-Link voltage rise to 1.3 p.u.
The performance of DC-Link voltage udc for the conven-
tional method is as shown in Figure 4(b). However, in
the new method, udc is almost constant, as shown in Fig-
ure 5(b). Because of the unbalanced power, a portion of
energy has stored in the wind turbine, thus, the rotor
speed
ω
w would enhance. But the rising is less than
0.08 p.u which is within the safe range, as shown in Fig-
ure 4(c) and Figure 5(c). With the failure to eliminate, it
turns back to the normal value.
Feedback law can generally be written as:
1()
()
uBx
Ax

v
(15)
where v is the equivalent input.
In order to eliminate and reduce the steady-state error
of the system, Equation (16) can be deduced from the PI
control.

12ref refref
vykyykyy dt
  
(16)
where yref is the reference value, k1 and k2 are the adjust-
able gains. 5. Conclusions
The control block diagram of the nonlinear DC-Link
voltage and the generator-side PWM converter is shown
in Figure 3. This paper proposes a low voltage ride through scheme
of PMSG wind power systems based on feedback lin-
earization. The DC-Link voltage is maintained and regu-
lated by generator-side converter. The control scheme of
the generator-side converter has been designed using
4. Simulation and Analysis
To verify the validity of the proposed algorithm, this
*
dc
u
dc
u
s
2
1
k
k
s
()
B
x
1
()Ax
rid
P
dc
u
*
g
P
g
P
*
s
q
i
s
q
i
ssqd sd
RiLi

s
q
u
*
0
sd
i
s
q
i
s
q
u
s
sdq sq
RiLi
dc
u
Figure 3.Control block diagram of the grid-side PWM converter.
J. WEI ET AL.
380
The
g
rid volta
g
e
0.50 1.00 1.50 2.00 2.50 3.00 3.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
Vrms
The grid voltage
(a) the RMS values of the gird voltage
The DC-Link volta
g
e
0.50 1.00 1.50 2.00 2.50 3.00 3.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
Udc
Udc
(b) the RMS values of the gird voltage
The rotor s
p
eed
t
s
0.50 1.00 1.50 2.00 2.50 3.00 3.50
0.80
1.00
1.20
w
ωw
(c) the rotor speed ωw
Figure 4. Simulation of the conventional method for power
system fault.
The
g
ird volta
g
e
0.50 1.00 1.50 2.00 2.50 3.00 3.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
V (p.u.)
The gird voltage
(a) the RMS values of the gird voltage
The DC-Link volta
g
e
0.50 1.00 1.50 2.00 2.50 3.00 3.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
Udc
Udc
(b) the RMS values of the gird voltage
The rotor s
p
eed
0.50 1.00 1.50 2.00 2.50 3.00 3.50
0.80
1.00
1.20
w
ωw
(c) The rotor speed ωw
Figure 5. Simulation of the new method for power system
fault.
feedback linearization, and the grid-side converter regu-
lates the power for MPPT. The simulation result demon-
strates the validity of the method. When the grid voltage
sags to 50%, the proposed algorithm can effectively de-
crease the rising of DC-Link voltage, and keep it almost
invariable so that the LVRT capability of PMSG wind
power systems is improved. Wind turbines can still run
in parallel operation until return to normal operating
condition during power system fault.
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