Modelling and Simulation of Load Connected Fixed
Blade Wind Turbine with Permanent Magnet
Synchronous Generators
Ahmed S. Al-Toma
(Ahmed.al-toma@brunel.ac.uk)
Maysam Abbod
(Maysam.Abbod@brunel.ac.uk)
Gareth A. Taylor
(Gareth.Taylor@brunel.ac.uk)
Brunel Institute of Power Systems, Brunel University London, Uxbridge, UB8 3PH, UK
iabc vabc
Vw
C
Vdc
Filter
G
ωm
PWM
PWM
Controller
Fig. 1 PMSG connected to the grid or load
Index Terms—Fixed Blade Wind Turbine, Load Connected,
Permanent Magnet Synchronous Generator.
I.
DC/AC
iabc
Grid / Load
AC/DC
Abstract- This paper presents the modelling and simulation
of a wind turbine driven Permanent Magnet Synchronous
Generator connected to a load. The system has been tested at
different wind speeds. The machine side controller has been
designed to match Maximum Power Point Tracking (MPPT) to
obtain high extraction of wind power when connected to a load,
while the load side controller fixes the DC voltage that is
converted to the AC load voltage. Detailed plots of voltage and
current profiles are also presented in the paper.
On the other hand, the battery is not necessary in case of
connection of wind turbine generator system to the grid due
to constancy of voltage and frequency in all points of grid.
INTRODUCTION
In recent years, there is a real orientation on production of
clean energy, especially wind energy to keep environment
within agreeable limit of constraints of noise and pollution.
This led to produce wind energy with multiple considerations
of control and protection to enhance the power system
generation in a good performance of generation quantities
such as voltage, frequency and power. To achieve that, wind
energy has been controlled during the operation process to
keep appropriate amount of power injected to the power grid
or stored in batteries. Squirrel-Cage Induction Generators
(SCIG) and Double – Fed Induction Generators (DFIG) are
typically used in fixed speed systems.
Generally fixed speed turbines are well-established,
simple, robust, reliable, cheaper compared to those
generators that used in variable speed Wind Energy
Conversion System (WECS). Due to continuous variation of
speed of wind during short period of time, the need of
variable speed generators becomes necessary. On the other
hand, Permanent Magnet Synchronous Generators (PMSG)
are most recently used in generation of electrical power from
the wind energy either in stand-alone operation or connected
to the grid as shown in Fig. 1.
In case of stand-alone, the connection of stored battery is
necessary to maintain the electrical power injection to the
building within rated limit in case of wind speed reduction.
II. WIND TURBINE MODEL
Wind energy is transferred to mechanical power through
wind turbine and hence to the electric energy through
generator. The kinetic energy in a flow of air through a unit
area perpendicular to the wind direction per mass is converted
to mechanical energy [1].
From Newton’s Law, the power captured by the wind
turbine for an air stream flowing through an area A, and then
generated by the wind is equal to [2]:
1
3
Pm  AV C p ( ,  )
(1)
2
where ρ is the air density of values 1.1 – 1.3 (kg/m3), A is the
area swept out by turbine blades (m2), V is the wind speed
(m/s), Pm is the wind power (watts or J/s) and Cp is the power
coefficient which can be expressed as a function of the tip
speed ratio λ and pitch angle β given by [3] [4] [5] [6]:
 .R
 m
(2)
v
where β is the pitch angle of the blade in degrees, R is the
radius of the area swept out by blades turbine and ωm is the
mechanical speed of the generator in rad/s. The power
coefficient can be expressed in (3):
C p ( ,  )  C1 (
1
C2
i
 C3   C4 )e
 C5
i
 C6
(3)
and
a
d
i 
ωs
1
1
0.035
(

)
  0.08  3  1
(4)
Vd
Id
The coefficients parameters of (3) are: C1 = 0.5176, C2=
116, C3 = 0.4, C4 = 5, C5 = 21, and C6 = 0.0068
In ideal case, the power coefficient Cp reaches a maximum
value equal to Cp = 0.593 which means that the power
extracted from the wind is always less than 59.3% and is
designed as Betz 's limit. In practice, values of obtainable
power coefficients are in the range of 40 %. This value below
the theoretical limit is caused by the inefficiencies and cause
by a various aerodynamic losses which depend on the rotor
construction (number and shape of blades, weight, stiffness,
etc.).
The performance power coefficient, Cp of a wind turbine is
plotted against the tip speed ratio (TSR) λ to get the
maximum values of Cp in all operation condition. Fig. 2
shows the plot of power coefficient with respect to tip speed
ratio (TSR) for different values of pitch angle β. It is observed
that the maximum power coefficient value Cp_max(λ,β)=0.48
for λ =8.1 in case of β = 0. This particular value of λopt results
in optimal efficiency point where maximum power is
captured from the wind by wind turbine.
Фf
Vq
Fig. 4 d-q and abc axis of typical PMSG
The output power is changed with the angular velocity ω
for variable values of the wind speed. Therefore, the optimum
values of P, Cp and λ should be taken in to account to get
optimum design as shown in Fig. 3.
III. PMSG MODELS
Dynamic modelling of PMSG can be described in
synchronous rotating reference frame where the q-axis is 90
degrees ahead of the d-axis with respect to the direction of
rotation. Fig. 4 shows the d-q and abc axis of typical model
of PMSG. The d-q stator voltages equations of this generator
are given by (5) and (6) respectively [7], [8]:
d f
di
(5)
v gd  Rg id  Ld d 
 e Lq iq
dt
dt
diq d f
(6)
v gq  Rg iq  Lq

 e ( Ld id   f )
dt
dt
where Lq and Ld are the inductances of the generator on the q
and d axis, Rg is the stator resistance, ψf is the permanent
magnetic flux and ωe is the electrical rotating speed of the
PMSG defined as [9]:
B=0
B=5
Cp
B=10
0.2
B=15
B=20
0.1
TSR
opt
0
0
2
4
6
8
10
12
14
16
e  ( pn / 2)m
18
TSR
Fig. 2 Variation of power coefficient with Tip speed
ratio for different values of pitch angle
6
x 10
4
3
Pm(w)
2
1
0
-1
In the same manner, a, b, c variables can be obtained from
the d,q variables through the Inverse of the Park’s
transformation as shown below:
sin t
cos t
1 Vd 
Va  
V   sin( t  2 / 3) cos(t  2 / 3) 1 V 
 b 
  q  (9)
Vc  sin( t  2 / 3) cos(t  2 / 3 1 V0 
-2
-3
100
200
300
400
500
600
Wm(rad/s)
700
800
900
(7)
where pn is the number of pole pairs of the PMSG and ωm is
the mechanical angular speed. Fig. 5 shows the equivalent
block diagram of special wind turbine under test. From Park’s
transformation, the d and q variables are obtained from a, b, c
variables as defined in (8):
Vd 
 sin t sin( t  2 / 3) sin( t  2 / 3)  Va 
V   2 cos t cos(t  2 / 3) cos(t  2 / 3) V 
 q 3
  b  (8)
V0 
 1/ 2
 Vc 
1/ 2
1/ 2
4
5
-4
0
b
q
Cp
max
0.3
0
Iq
c
0.5
0.4
θ
1000
Fig. 3 the Output Power with respect to ω
for variable generator speed
2
where ωt = θr is the rotor angular position.
The equation of electromagnetic torque can be obtained
from the input power that is transferred through the air gap
from the stator. The total input power that transferred from
the stator is expressed in (10):
Pin  Vsaia  Vsbib  Vscic
A. Machine Side Converter Control(MSC)
In Machine side Converter, the controller is operated by
two loops, inner and outer loops. In the inner loop, the d-q
components currents have been controlled by adjusting
appropriate values of currents reference. This part of
controller has achieved the electrical dynamic of the machine.
In outer loop, the mechanical dynamic has been controlled by
adjusting the value of the optimum angular speed of the
machine ωg. In this case the optimum speed has been
controlled by selecting optimum value of tip speed ratio with
respect to wind speed to ensure that the machine is running
at optimum speed in any case of wind speed change and any
transient will be overcome at any instant.
It is obvious from (16), the electromagnetic torque has
been influenced by iq , so it is easy to control this torque by
controlling angular velocity which finally control quadrature
axis current iq. By choosing a set point of angular velocity
ωg, the maximum power point tracking have been done to
get maximum power capturing from the wind during any
change in wind speed.
Since the system type is first order equation, Proportional
Integral (PI) controller has a good effect to use in this case.
This controller has a proportional parameter KP and
integrator parameter KI, which have to be tuned in a proper
way to get the optimum operation and response. The
commanded q-reference current iqref is determined by speed
controller and the output of PI controller is:
(10)
where Vsa , Vsb , Vsc are stator voltages.
When the d-q reference quantities are rotate at ωr=dθ/dt,
then the equation of the input power is transferred to the rotor
is reduced in (11):
3
(Vd id  Vq iq )
2
Pin 
(11)
where zero sequence quantities are neglected, the output
power can be expressed in (12) :
Pout 
3
(r Ld id iq  r miq  r Lqiqid )
2
(12)
For the angular speed rotates with p number of poles, then
the electrical speed in term of mechanical is ωr=(pn/2)ωm .
Then the output power can be deduced to (13) with pn number
of pole pairs:
Pout 
3
pnm ( Ld id iq   miq  Lqiqid )
4
(13)
By dividing the output power by ωm, the electromagnetic
torque (Te) equation can be obtained by (14):
Te 
3
pn ( Ld id iq   miq  Lqiqid )
4
iqref  K p e  K I  e dt
(14)
where Kpω and KIω are the proportional and integral
parameters of PI controller, while eω is the error between the
reference speed and measured speed of generator.
Depending on the q-axis reference current, the d-q
controlled output voltage can be determined by the PI
controller as shown below:
If p is the number of pole pairs in the machine then the
electromagnetic torque can be expressed in (15):
Te 
3
p(( Ld  Lq )id iq   m iq )
2
(15)
In addition, if it is a reasonable approximation where
PMSG is assumed to be wound-rotor, then Ld= Lq, and the
expression of the electromagnetic torque in the rotor can be
described in (16) as [10]:
Te 
3
pn f iq
2
d m
 Te  Tm  F m
dt
(17)
where J is the total moment of inertia, F is the viscous
friction coefficient and Tm is the mechanical torque developed
by the turbine.
IV.
V *d  K pied  K Ii  ed dt  r Lqiq
(19)
V *q  K pi eq  K Ii  eq dt  r ( Ld id  m )
(20)
where, Kpi and KIi are the a proportional and integral
parameters gain of the current loop PI controller
respectively, while ed and eq are the error of d-q current
component as shown in (21) and (22) respectively :
(16)
The dynamic equation of the wind turbine is given in (17):
J
(18)
ed  idref  id
(21)
eq  iqref  iq
(22)
The controlled output voltages V*d and V*q are transferred
to abc voltages by means of Park inverse transformer to get
the controlled values of 3-ph voltage which adjust the PWM
to generate pulses of converter.
CONTROL SCHEMES OF THE SYSTEM
Since the output voltage and frequency have to be constant,
the control system has been designed to perform that in both
machine side and load side to keep all quantities within
acceptable limit.
B. Load Side Converter Control(LSC)
In load side control, the DC voltage has been converted to
AC by triggering 6-pulses IGBT device by PWM generator.
3
The values of triggered voltages have been selected by a
proper value of DC link capacitor and inductor that can do
this task. DC battery is able to supplement and maintain the
voltage to the load when the wind speed is reduced to lower
values. The setting value of the DC voltage through the
capacitor, the output AC voltage will be fixed by controlling
the output load currents that will be the input of the load side
controller.
In order to obtain only the active power to be transferred to
the load, iq is adjusting and set to be zero. As well as current,
the output voltages have been used in control system by
Phase-Locked Loop (PLL) to maintain the phase shift of the
voltages in synchronization with the line during the control
process.
battery have been fixed in the Simulink model as shown in
Fig. 9.
The first simulation for variable wind speed has operated
in case of R-L filter. Then simulation has been done with this
model of wind speed of 8, 12, 10 m/s to analyse the
behaviour of the wind turbine when its operating point is less
than the rated wind speed. The second simulation has been
done with LCL filter. It is obvious that the system is operated
well during the wind speed change. The generated voltages
and currents and also the output of the voltages and currents
are shown in Fig 10- 13.
V. SIMULATION AND RESULTS
In this work, the modelling of single machine, 3-phase
fixed blade horizontal axis wind turbine direct train is
connected to permanent magnet synchronous generator fed a
load. The modelling has been done in Matlab/Simulink
program to achieve the output results in time domain [10].
All parameters of the system have been used in real value to
keep the system operation in real simulation and to avoid the
conversion of real values to per unit values. The data of Table
I have been applied to satisfy above model.
Fig. 5 Wind Turbine model
15
12
Vw(m/s)
TABLE I
WIND TURBINE GENERATOR SYSTEM PARAMETERS
Wind Turbine Parameters
Radius of blade ( R )
6m
Density of the air ( ρ )
1.11
Rated wind speed Vwind
12 m/s
Maximum power coefficient (Cp)
0.48
Optimum Tip speed ratio ( λ )
8.1
PMSG parameters
Stator resister (Rs)
0.25 Ω
Stator inductance (Lq=Ld=L)
0.6857 mH
Permanent flux
0.0534 Wb
Number of pole pairs (p)
24
Moment of inertia ( J )
0.0001295 Kg.m3
Friction coefficient ( F )
0.0001 N.m.s
DC Link
DC link Voltage
760 V
Capacitor ( C )
2.2 mF
Inductor ( L )
0.5 mH
8
4
0
0
2
4
6
8
10
T(s)
Fig. 6 Variation of Wind speed with time
600
500
Wm(rad/s)
400
300
200
The generator is connected to the load through full load
back-to-back IGBT converter which converted power AC/DC
to control the output power of wind turbine. This voltage has
been converted finally by the DC/AC inverter connected to
the load. In the beginning of simulation, wind turbine shown
in Fig. 5 has been tested and subjected to infinite values of
the wind speed to get the variation of mechanical power and
torque. It is shown that the wind turbine operates with rated
wind speed of 12 m/s.
The variation of wind speed Vw of the wind turbine with
respect to time is shown in Fig. 6. The output mechanical
power and torque that entered to PMSG are shown in Figs. 7–
8. The complete system includes: wind turbine, PMS
generator, rectifier, inverter and normally closed switch of
100
0
0
2
4
6
8
10
T(s)
Fig. 7 Variation of the output power (W) with respect
to time
4
600
50
400
200
0
Te
Tm
Vg abc
Tm &Te(N.m)
100
-50
0
-200
-100
-400
-150
0
2
4
6
8
-600
3.995
10
T(s)
4
T(s)
4.005
Fig. 10 Generated 3-ph voltages with respect to time
(High resolution time frame)
Fig. 8 Variation of the Mechanical torque (Tm) &
Electromagnetic torque (Te) (N.m) with respect to time
100
Ig abc
50
0
-50
-100
3.995
4
T(s)
4.005
Fig. 11 Generated 3-ph currents with respect to time
(High resolution time frame)
800
600
VLoad abc (v)
400
200
0
-200
-400
-600
-800
0.03
0.031
Time (seconds)
Fig. 12 A 3-ph Load voltages with respect to time
with RL filter (High resolution time frame)
60
40
I Load (A)
20
0
-20
-40
-60
0.03
0.0304
Time (seconds)
0.0308
Fig. 13 A 3-ph Load currents with respect to time
with RL filter (High resolution time frame)
Fig. 9 The complete system of Wind turbine PMSG connected to load
5
0.031
775
be stable after a small oscillation which depends upon the
size of dc link capacitor and inductor. It is also concluded
that, load side converter with LCL filter is suitable in
smoothing of load voltages and currents rather than RL filter.
It is also obvious that the PI controller is regarded as an
attractive solution for adjustable speed wind generator and
then the profile of output voltages and currents especially for
constant load.
With regard to further work, the connection of PMSG or
DFIG to the grid will be investigated, modelled and simulated
as well as applying other types of controller such as slide
mode or hysteresis current controller to overcome oscillations
in output currents.
770
Vdc (v)
765
760
755
750
745
0
0.01
0.02
0.03
Time (seconds)
0.04
0.05
Fig. 14 DC Voltage of the rectifier converter
(High resolution time frame)
REFERENCES
The DC voltage maintains constant during the operation as
shown in Fig. 14. The 3-ph voltages and current of LCL filter
are shown in Figs. 15-16.
[1] J. Zaragoza, J. Pou, A. Arias, C. Spiteri, E. Robles, and S. Ceballos,
“Study and experimental verification of control tuning strategies in a
variable speed wind energy conversion system,” Renewable Energy,
vol. 36(5), pp. 1421-1430, 2011.
800
[2] T. Ackermann, “Wind Power in Power System, West Sussex, England”:
John Wiley and Sons, Ltd, 2005.
600
V Load abc (v)
400
[3] M. Mansour, M. N. Mansouri, M.F. Mmimouni, “Study and control of a
variable-speed wind-energy system connected to the grid”, International
Journal of Renewable Energy Research, vol. 1(2), pp. 96-104, 2011.
200
0
[4] M. Cirrincione, M. Pucci, and G. Vitale, “Neural MPPT of variable
speed wind generators with induction machines in a wide speed range ”,
Proceedings in IEEE Conference on Energy Conversion Congress and
Exposition, pp. 857-864, 2011.
-200
-400
[5] A. K. Singh, R. Krisham, and Y. Sood, “Modeling and Control of Grid
Connected Variable Speed PMSG Based Wind Energy System”,
Conference on Advances in Communication and Control Systems 2013
(CAC2S 2013), Published by Atlantis Press.
-600
-800
0.03
0.0302
0.0304
0.0306
Time (seconds)
0.0308
Fig. 15 A 3-ph Load voltage with respect to time
with LCL filter (High resolution time frame)
[6] B. Muhando, T. Senjyu, H. Kinjo, and T. Funabashi, “Extending the
modelling framework for wind generation systems: RLS-based
paradigm for performance under high turbulence inflow” IEEE
Transactions on Energy Conversion, vol. 24(1), pp. 211-221, 2009.
50
40
[7] K. Tan, and S. Islam, “Optimum Control Strategies in Energy
Conversion of PMSG Wind Turbine System without Mechanical
Sensors”, IEEE Transactions on Energy Conversion, vol. 19(2) p392399, June 2004.
30
I Load abc (A)
20
10
[8] L.G. Gonzalez, E. Figueres, G.Garcera, O.Carranza, “Modelling and
control in wind energy conversion systems(WECS)” 13th European
Conference on Power Electronics and Applications, EPE ,2009.
0
-10
-20
[9] Y. Errami, M. Hilal, M. Benchagra, M. Ouassaid, M. Maaroufi,
“Nonlinear Control Of MPPT and Grid Connected for Variable Speed
Wind Energy Conversion System Based on the PMSG” Journal of
Theoretical and Applied Information Technology, vol. 39(2), 2012.
-30
-40
-50
0.03
0.0302
0.0304
0.0306
Time (seconds)
0.0308
[10] Y. Errami, M. Ouassaid and M. Maaroufi, “Modelling and Control
Strategy of PMSG Based Variable Speed Wind Energy Conversion
System” International Conference on Multimedia Computing and
Systems (ICMCS), 2011.
Fig. 16 A 3-ph Load currents with respect to time
with LCL filter (High resolution time frame)
VI. CONCLUSIONS AND FURTHER WORK
Horizontal axis Wind turbine fully decoupled PMSG
connected to load has been simulated in Matlab/Simulink.
From simulation, it is concluded that the wind turbine
generator system is controlled well to get MPPT in generator
side controller. Also smooth DC voltage in load side
controller has been achieved. The outputs of voltages and
currents show that there is a small distortion in output current
due to inductance of R-L filter. The DC output voltage will
6