Engineering, 2013, 5, 96-100
doi:10.4236/eng.2013.51b017 Published Online January 2013 (http://www.SciRP.org/journal/eng)
Simulation and Analysis of PMSG-based Wind Energy
Conversion S ystem using D if f eren t Covert er Mod els
Hua Ye1, Juan Su1, Songhuai Du2
1SENSE Lab, Technical University of Berlin, Berlin, Germany
2Department of Electrical Engineering, China Agricultural University, Beijing, China
Received 2013
Abstract
Modeling of a permanent magnet synchronous generator (PMSG)-based wind energy conversion system is presented
for the simulation of diverse transients. In order to perform multi-scale transients, the back-to-back voltage source con-
verter (VSC) is modeled using three different forms including the detailed, switched and average models. The
PMSG-based WECS is implemented in PSCAD/EMTDC. The simulation results show that the detailed and switched
model of VSC give a detailed and accurate representation, while the average model pr ovides an efficient simulatio n.
Keywords: Pow er system simulation, PMSG, Wind power generation, Voltage source converter, Multi-s cale transients
1. Introduction
Modeling and simulation is an essential step for the de-
sign and operation of modern power systems including
distributed energy resources. As a result of increasing
environmental concern, wind energy conversion system
(WECS) is becoming the most competitive form o f e lec-
tricity generation from renewable sources. Within con-
cepts of WECS, the permanent magnet synchronous ge-
nerator (PMSG)-based direct driven WECS has advan-
tages over the other concepts in terms of the energy yield,
reliability and ma i nte na nc e problem [1].
Usually, a PMSG-based WECS is composed of me-
chanical, electrical, and control subsystems whose time
constants vary from microseconds to minutes or even
more. For example, power electronic converter performs
high-frequency transients due to its high-frequency
switc hi n g. At t he sa me t i me, t he dynamic behavior of the
wind turbine shows a slow change. The use of detailed
switching models often leads to significant increase of
computatio nal times. On the contract, the power system
dynamic simulation does not account for fast transients
and ha rmonics.
A typical schematic representation of this wind po wer
generation s ystem is dep icted in Figure 1. The PMSG is
conne cted a t the p oint o f co mmon co uplin g (PCC) to the
utility grid via a back-to-back two-level voltage source
converter (VSC) and a step-up transformer. For purpose
of analysis, the PMSG-based WECS is divided into two
parts. The back-to-back VSC p r es ents the hi g h-frequency
transients, which is hatched in a shadow. The rest part of
this system is considered as slow part presenting
low-frequency tr ansi ents .
In this paper, modeling and si mulation of the compo-
nents in this PMSG-based WECS is developed. In order
to analyze mulit-scale transients, three alternative forms
of the VSC using the detaile d, switched [2] and average
models [3] are represented. Through the simulator
PSCAD/EMTDC, this PMSG-based WECS is imple-
mented by employing different models of the VSC.
PMSG
3
AC
DC
DC
AC
PCC
Grid
utility
Generator side
controller Grid side controller
Figure 1. T he schematic represe ntation of a PMSG -based
WECS unit.
This paper is organized as follows. A PMSG-based
WECS is described in Section II. In Section III, three
different models of VSC are represented and compared.
A test case is performed in Section IV. Conclusions are
drawn in Section V
2. PMSG-based Wind Power Conversion
Syste m
2.1. Aerodynamic and Mechanical s ystems
The operational performance of wind turbine can be

H. YE ET AL.
97
modeled through a mathematical relation between the
wind speed
w
V
and mechanical power extracted as fol-
lows:
23
wtw p
0.5( ,),P rVC ρπλ β =
(1)
where wt P is the extracted power from the wind,
ρ
is
the air density,
r
is the blade radius, and
p
C
is the
power coefficient which is a function of both tip speed
ratio,
λ
and blade pitch angle,
β
.
Numerical approximations have been developed to
calculate
p
C
as follows:
21
p116
(,)0.51760.45 e0.0068 ,
i
i
C
λ
λββ λ
λ
−

=−− +


(2)
with
3
110.035 .
0.08 1
i
λλ β β
= −
++
(3)
If the air density and blade swept area are invariable,
wt
P
depends on the tip speed ratio and the turbine speed.
The maximum output power of the wind turbine is
calculated at the maximum power conversion coefficient
p max
C
and the optimal tip speed ratio
opt
λ
:
3
23
t
wt maxp maxoptt
opt
0.5 ,
r
P rCk
ω
ρπ ω
λ

= =



(4)
where
( )
3
2
optp maxopt
0.5 /krC r ρπ λ =
, and t ω is the
angular speed of the wind turbine blade. The maximum
power is obtained by regulating the turbine speed with
respected to the wind speed such that the maximum
power point tracking (MPPT) can be achieved. The
MPPT gives the reference power,
ref
P
, for the grid side
converter discussed hereafter.
In recent years, direct-driven PMSG has gained
considerable interest due to its advantages including no
gear maintenance, reliability and efficient energy
production. Thus, analysis of dynamic characteristics of
the driven-train is becoming a concern of utmost
importance. In this paper, the driven-train is represented
by one-mass mode l:
twt g
d ()() (),
d
t
JT tTt
t
ω
= −
(5)
where
J
is the combined inertia o f tur b ine a nd ge ne ra to r ,
wt
T is the aerodynamic torque produced by the turbine,
and
g
T
is the electrical tor que.
2.2. PMSG Representation
The computations associated with the PMSG modeling
in abc reference frame are complicated and lengthy.
Usually, the dq0 or Park transformation is applied in the
PMSG modeling. The electromagnetic equations of
PMSG are described based on the dq0 reference frame in
which the
q
axis rotates synchronously with the
magnet flux
f
ψ
as follows:
sd
sdsds sdgsq sq
sq
sqsqs sqgsd sqgf
d ()()() ()(),
d
d ()()()()()() ,
d
it
Lvt RittLit
t
it
Lvt RittLitt
t
ω
ω ωψ
=−+
=−+ −
(7)
where sd L,
sq
L
and s R are the generator inductances
and resistance, respectively.
g
ω
is the angular speed of
the gener ator.
2.3. Control System
1) Generator-side controller: the control strategies
applied to the generator-side converter is schematically
expressed in Figure 2, where the direct current vector
control mechanism is adopted. The terminal currents of
the PMSG are used as input signals to the generator -side
controller.
As one of the salient features, the DC-link voltage is
controlled by the generator-side controller instead of the
grid-side controller. When a network disturbance occurs,
the controller keeps the generated active po wer of PMSG
at the appropriate level to avoid DC-link overvoltage.
Meanwhile, the reference of d-axis current is set to zero
to avoid the demagnetization of permanent magnetic.
The corresponding reactive power output of PMSG is
zero.
( )
2
0.5 
*
dc
v
( )
2
0.5 
dc
v
+-
g
ω
*
g
T
r
2
3p ψ
+-
*
q
i
++
g ddr
()Li ωψ +
g
ω
∫
ABC
/DQ
+-+-
g qq
Li ω
*
d0i=
control
signal
generator
g
θ
g
θ
PI
sabc
i
PI
PI
ga
S
gb
S
gc
S
Figure 2. Cont rol bloc k for the generator-side converter.
2) Grid-side controller: the block diagram of the
grid-side controller is shown in Figure 3. The direct
current vector control mechanism is also adopted for the
control desi gn.
The active power reference
ref
P
is de termined in such
a way to provide the maximum power to the grid through
the MPPT as mentioned earlier. In this study,
ref
P
varies depending on the level of terminal voltage during
the times when the voltage drops below 0.9 p.u. This
situation is used to supply appropriate power to the grid
when a network disturbance appears. Meanwhile, it can
avoid the overvolt age in the DC-link circuit.

H. YE ET AL.
98
ABC
/DQ
labc
i
labc
v
PLL
L
θ
grid power
calculation
d
,i
q
i
d,v
q
v
grid
Q
grid
P
+-
*
d
i
++
ds qq
v Li ω −
+-++
qs dd
v Li ω +
*
q
i
control
signal
generator
s
θ
q
i
-+
ref
Q
grid
Q
-+
d
i
grid
P
RMS
>
ref
P
r
ω
MPPT
grid
v
0.9
ref grid
Pv×
Fault conditions
0.9 1
0.9 0
>→
<→
1
0
Normal conditions
PI
la
S
lb
S
lc
S
PI
PI PI
Figure 3. Block diagr am of the grid-side controller.
3. Three Different Models of AC-DC-AC
Voltage Source Converter
In PMSG-based WECS, a back-to-back VSC is usually
used to link the direct drive synchronous generator and
the utility grid. The response of such power electronic
converter to a disturbance is characterized by very high
frequency phenomena. In spite of this, due to the
objective of different studies, a voltage source converter
is currently modeled with different ways in power
system simulations. The topology of the back-to-back
VSC comprises a double conversion from AC to DC and
then from DC to AC. For the sake of analysis, only
generator-side VSC is represented in the following, and
the gri d-side VSC is developed in an analogous way.
3.1. Detailed Mod el
In this case, the ac-to-ac converter is schematically
expressed by using actual power semiconductor device
models. As shown in Figure 4, this detailed model is
composed of 6 IGBTs and 6 anti-parallel diodes. Since
the simulation is mainly performed at the circuit level,
a very detailed presenta tion of the back-to-back VSC
can be obtained. For instance, t he har monics generated
by the VSC can be precisely represented. This is in-
structive for the production design associated with the
wind power generation.
However, these models in some simulator like
Pspice are described as a nonlinear controlled source
by means of functions that contain exponential terms.
It result s slow execution times, large amounts of gen-
erated data, and co nverge nce pro blem [4]. Based on the
circuit configuration, t he mo deling in Matlab Simulink
involves differential equations that are resolved
through state space method. From the viewpoint of
wind farm, a large number of differential equations
exist, and thus the computations are cumbersome and
time-co nsuming.
S1
D1
S3
D3
S5
D5
S4
D4
S6
D6
S2
T2
a
b
c
dc
v
+
-
a
i
b
i
c
i
dc
i
Figure 4. VSC co nfiguration.
3.2. Switched Model
The switching func tion concept is use d to describe the
performance o f t he act ual po wer co n verter s. As a result,
the ac-to-ac converter is modeled according to the
functions rather than circuit topologie s [2]. Since it
does not refer to single switch element, the s wi tching
can be easily modeled.
Figur e 5 sh ows an equivalent model where switches
are replaced by three voltage sources on ac side and a
current source on dc side. The voltage sources are a
func tion o f the D C-link voltage
dc
v
and the switching
functi ons .
ga ga
gb dcgb
gc gc
2 -1 -1
1-1 2 -1,
3-1 -1 2
vs
vv s
vs
 

 

=
 

 


 
(8)
where
ga
s
,
gb
s
and
gc
s
are the switching functions that
uses the 6 IGBT pulses as control input. Herein, the si-
nusoidal pulse-width-mod ulation (SP WM) control strat-
egies are used to generate the IGBT pulses. The DC-link
current source is defined as a function of the ac side cur-
rents and the swi tchi ng functio ns:
a
dcga gbgcb
c
.
i
iss si
i



=



(9)
+
-
+
-
+
-
a
b
ccontrolled
voltage
sources
ga
v
gb
v
gc
v
dc
v
SPWM
ga
s
gb
s
gc
s
a
i
b
i
c
i
+
++
dc
i
dc
v
+
-
a
i
b
i
c
i
power flow
signal flow
reference
signals
Figure 5 . Sw itching functio n model of VSC.

H. YE ET AL.
99
The switched mode l can corr ectly represe nt the main
components of the electromagnetic transients and har-
monics generated by the VSC. The switching frequen-
cy of VSC can reach several kHz, and t hu s a s mal l ti me
step size in the order of microseconds is used in the
simulation. This is not suitable for power system dy-
namic simulation studies. Therefore, a low-frequency
representation of the behavior of the converter is re-
quired.
3.3. Average Model
Figure 6 presents an average model of the VSC. The
three reference signals replacing the switching functions
are used to represent three average volta ge so urces o n ac
side. Correspondingly, the current source is calculated
based on power balance by negle ct i ng the i nte r na l lo ss of
VSC.
+
-
+
-
+
-
a
b
c
controlled
voltage
sources
ga
v
gb
v
gc
v
dc
v
a
i
b
i
c
i
dc
i
dc
v
+
-
a
i
b
i
c
i
power flow
signal flow
reference
signals
power
calculation
ga
v
gb
v
gc
v
dc
v
ac
P
ac
dc
P
v
Figure 6 . Averag e model of VS C.
This average model is well suitable for the simulation
of slow transients [5]. A large time step can be used so
that much more efficie nt simulatio n is achie ved. Howev-
er, this model does not represent high-frequency tran-
sients and harmonics.
4. Test Case Studies
A PMSG-based WECS is simulated and analyzed when
subjected to the system faults. Figure 7 shows the
PMSG-based wind power unit connected to the utility
grid via a step-up transformer and transmission line.
This PMSG-based WECS was implemented in
PSCAD/EM T DC, where the above three different
converter models are used se parately for the purpose of
comparison.
The grid operation under vario us condit ions ha s a sig-
nificant impact on the wind power generation. In this
study, it is o f prime interest to investigate the lo w voltage
ride through (LVRT), which is critical to the design of
the PMSG-based WECS. A three-phase-to- ground fault
was applied to the middle of the trans mission line, and it
was self -cleared after 0.16 s. For the sake o f anal ysis, the
win d speed is maintained constant at 10 m/s.
AC-DC-AC
converter
PMSG
turbine
faults utility grid
L
P
L
Q
controllers
La,b,c
v
g
P
Figure 7. A PMSG-base d wi nd power unit.
For the purpose of comparison, the followi ng three al-
ternative forms of representation of AC-DC-AC conver-
ter are included in the implementation of WECS se pa-
rately.
• The detailed model;
• The switched model;
• The average model.
(a) Simulation using the detailed model of VSC
(b) Simula tion using the switched model of VSC
(c) Simulation using the average model of VSC
Figure 8. Active and reactive power produce d by the
PMSG-based WEC S.
Figure 8 shows plots of the power produced from the
PMSG,
g
P
, and the real and reactive power injected into
the utility grid,
L
P
and
L
Q
. Plots in Figur es 8(a)-8(c)
are obtained from the above three alternatives, respec-

H. YE ET AL.
100
tively. At
t
= 0.2 s, a three-phase-to-ground fault oc-
curred. Due to the generator-side controller, the PMSG
output power keeps an agreement with the one required
by the grid side. Hence, this can avoid the oscillation of
DC-link voltage as shown in Figure 9. In Figure 8(a),
the value of
L
P
is lower than
g
P
as the internal loss of
detailed model of the VSC is not neglec te d. As seen fr om
these results, there are no visible differences using the
three converter models.
Figure 9. DC-link voltage.
(a) Simulation using different models of VSC
(b) Zoom-in results using different models of V SC
Figure 10. Grid-side VSC terminal voltage on ac s ide.
As shown in Figures 10 and 11, high-frequency tran-
sients such as harmonics are well represented using the
detailed model of the VSC. Ho wever, the average model
neglects the effect of fast switching and the small-signal
characteristics are extracted. In order to evaluate simula-
tion efficiency, the computational times using the above
three different VSC models are summarized in Table I.
Due to the detailed representation of circuit configuration,
the computatio nal time with the detailed model is greatly
increased compared to the switched model with the same
simulation time step. However, the average model pro-
vides significant savings in computational time com-
pared to the other models.
Table 1. Comparison of simul ation time using different
VSC models.
VSC models Detail ed
model Switched model Average model
Time step size 20
s µ
20
s µ
200
s µ
Compuational time 35. 5 s 15.06 s 1.45 s
5. Conclusions
Modeling of a PMSG-based WECS was presented for
the accurate or efficient simulation of diverse transients.
Each of the components covering the mechanical, elec-
trical and co ntrol subsystems was modeled. Although the
back-to-back VSC contains high-frequency transients
occurring, the average VSC model was included for dy-
nami c s simula tion leading to a high computational effi-
ciency. In order to perform the high-frequency transients
accurately, the detailed and switched models of VSC
were used
This PMSG-based WECS was implemented in
PSCAD/EMTDC using the detailed, switched and aver-
aged models of VSC, respectively. The results shows
that the detailed and switched models give accurate si-
mulation, but have an increased computational cost. At
the same time, the average model provides an efficient
simulation, but does not give detailed si mulation. T here-
fore, an innovative model is required to bridge the simu-
lation of diverse transients in the same simulation run.
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