Sustainable Energy Technologies and Assessments 19 (2017) 114–124
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Sustainable Energy Technologies and Assessments
journal homepage: www.elsevier.com/locate/seta
Original article
Design, modeling and simulation of variable speed Axial Flux Permanent
Magnet Wind Generator
Sriram S. Laxminarayan a,⇑, Manik Singh a, Abid H. Saifee b, Arvind Mittal a
a
b
Energy Centre, Maulana Azad National Institute of Technology, Bhopal, India
Dept. of Electronics and Communication, All Saints’ College of Technology, Bhopal, India
a r t i c l e
i n f o
Article history:
Received 15 June 2016
Revised 19 October 2016
Accepted 12 January 2017
Keywords:
Axial Flux Permanent Magnet Generator
Single Stator Double Rotor
Horizontal Axis Wind Turbine
MATLAB/Simulink
Modeling
Simulation
a b s t r a c t
Variable speed wind energy systems using permanent magnet generators are increasingly becoming popular for both standalone and grid connected applications. Axial Flux Permanent Magnet Generators
(AFPMG) are a relatively new class of generators which are being considered as effective alternative to
conventional Radial Flux generators, especially in wind applications, owing to their special features
and attractive benefits. This paper presents the design of an Axial Flux Permanent Magnet Generator well
suited for variable speed wind applications. A 2000 VA, 240 V, 3 phase, 10 pole, 5 rps AFPMG with Single
Stator Double Rotor configuration has been considered for the design and analysis. The behaviour of the
AFPM wind generator is investigated for different wind conditions, through dynamic modeling and simulation. The comprehensive modeling of AFPMG along with the details of the models for the Horizontal
Axis Wind Turbine (HAWT), drive train, speed controller and pitch controller have been presented. The
complete system model is implemented on MATLAB/Simulink platform and simulations are carried out
for various wind conditions. The response of the generator for both constant wind input and variable
wind pattern have been presented and discussed. The functioning of pitch controller is also verified for
high wind speed conditions.
Ó 2017 Elsevier Ltd. All rights reserved.
Introduction
In the prevailing global energy deficit scenario, generating
energy from renewable energy sources has emerged as the most
viable and sustainable solution. Although the presence of renewable energy systems is ubiquitous in the present landscape of
energy, the renewable energy sector is still beset with many technical issues. However, a strong commitment exists to address such
issues and make the renewable energy option attractive and competitive compared to the conventional energy systems. In line with
this, significant efforts are being made to maximise the production
of energy from renewable energy sources while keeping the prime
focus on improving their associated economic aspects.
Among the renewables, wind energy has historically been a
front runner for both large scale and small scale applications, still
holding huge scope for exploitation in many parts of the world.
Wind energy conversion systems have undergone vast transformations over the years, achieving remarkable technical progress and
is presently considered a matured technology [1]. Traditional wind
⇑ Corresponding author at: ‘Anugraha’, SARA 59-A, Puthen Road, Vazhappally Jn.,
Fort P.O., Trivandrum, Kerala, 695023, India
E-mail address: sriram.fort@gmail.com (S.S. Laxminarayan).
http://dx.doi.org/10.1016/j.seta.2017.01.004
2213-1388/Ó 2017 Elsevier Ltd. All rights reserved.
energy systems have been constant speed systems which were
designed to give their optimal performance at certain wind speeds.
They use gear boxes to couple the wind turbine with the generator
and hence suffer a lot of related problems such as complexity in
their control, high fatigue, noise and maintenance requirements.
The newer wind energy systems have therefore moved on to gearless direct drive concept in which the turbine and generator are
coupled directly without a gear box. Such systems, known as variable speed systems, have superior low speed performance and
improved energy capture capability [2]. However, variable speed
systems require a generator with a large number of poles since
the speed of operation would be lower, limited by the directly coupled wind turbine.
With the advent of high strength permanent magnets and the
remarkable advancements that occurred in their field lately, electrical machines using permanent magnets have been increasingly
sought after owing to their relatively simple design, compact structure and robustness. Permanent magnet generators have been
found most suitable for variable speed systems wind systems since
their construction allows the inclusion of a large number of poles
easily which would have been difficult in the case of conventional
field excited generators [3,4].
S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124
Axial Flux machines with conventional field poles machines
were developed almost a century ago, though their successful foray
into the field of electric machines was hindered owing to certain
complexities involved in their construction and difficulties
encountered in providing ventilation. Hence, traditionally electric
machines have been commonly of radial flux type. However, the
huge popularity of permanent magnet generators has kindled an
immense interest in Axial Flux Permanent Magnet Generators
(AFPMG) recently, since the use of permanent magnets enables
easier design and construction. These machines hold a promising
future, offering many exciting features and advantages over radial
flux machines. They have been brought into the limelight of active
research ever since, with commendable studies already been conducted on its performance and applications, especially as generators in wind energy conversion systems [5,6].
From the comprehensive literature survey conducted on the
subject it is seen that abundant work has been carried out in terms
of designing and modeling of permanent magnet machines, albeit
majority of them consider radial flux machines. The relatively lesser research efforts intended towards axial flux machines seem to
focus on the physical design, design optimization, thermal analysis
etc. using various tools and techniques. Various electromagnetic
and mechanical design procedures for Axial Flux Permanent Magnet Generators of different topologies have been discussed in [6–
10]. The studies presented in [11–13] deal with the modeling analysis of permanent magnet generators of radial flux type in variable
speed wind systems while those presented in [14–16] deal with
analytical modeling of Axial Flux Permanent Magnet machines. It
can be seen that comprehensive studies comprising design of an
AFPMG for wind systems, both the mathematical and tool based
dynamic modeling of the entire system and subsequent simulation
studies to understand the generator characteristics, is fairly limited. In this paper, an Axial Flux Permanent Magnet Generator
(AFPMG) has been designed, which is most suited to be used as a
wind generator in variable speed systems. Then, the mathematical
model of the system consisting of the AFPMG directly coupled to a
pitch controlled Horizontal Axis Wind Turbine (HAWT) is obtained
and is implemented in MATLAB/Simulink platform. Simulations
have been carried out to examine the behaviour of the wind generator under different wind speed conditions and the results have
been discussed.
is sandwiched between two rotors carrying permanent magnet
poles [22,23]. The arrangement of permanent magnets is in such
a way that the North Pole of one rotor faces the South Pole of the
other rotor and vice versa (NS-SN configuration). The unique feature of this particular configuration is that the magnetic flux passes
from one rotor to the other crossing the stator axially completing
the magnetic circuit, without passing through the stator disc itself
in a radial direction, i.e., the stator disc does not necessarily serve
any purpose for the path of the magnetic flux, other than supporting the three phase windings. This allows the generator to have a
non-magnetic non-conducting material such as plastic or wood
for the stator disc, making it lighter in weight. This also eliminates
iron losses and makes the machine more efficient.
Design of Axial Flux Permanent Magnet Generator
The AFPMG under consideration has a SSDR structure with NSSN configuration for permanent magnets as shown in Fig. 1. This
configuration of the AFPMG makes it most suitable for wind applications since the short axial length of the machine enables it to be
comfortably accommodated in the nacelle of the wind turbine
(which usually has space constraints). Since the machine is compact, a nacelle of smaller size could be employed. Also, lesser
weight of the generator would mean that the weight of the nacelle
is reduced. Moreover, it offers a higher power density and higher
efficiency since iron losses are absent.
The AFPMG has been designed following the fundamentals of
permanent magnet machine design [24,25] and the basic design
equations have been presented below.
The sizing equation of the AFPMG is given by
Pout ¼
p2
8
Bav ac 1 k2 ð1 þ kÞ D3so Ns
ð1Þ
where Pout is the output power Bav is the average air gap flux density
or specific magnetic loading (chosen as 0.6 Wb/m2), ac is the specific electric loading, Dso is the outer diameter of stator, Ns is the
speed of rotation and k is the diameter ratio, which is the ratio of
inner diameter (Dsi Þ to outer diameter of stator ðDso Þ.
Considering the disc forms of stator and rotor, the specific electric loading is worked out as,
Axial Flux Permanent Magnet Generator (AFPMG)
In an AFPMG, the stator and rotor are in the shape of discs
stacked or mounted on a shaft and the magnetic flux traverses
from one disc to the other in a direction parallel to the shaft (i.e.
axial direction). When compared to their Radial Flux counterparts,
Axial Flux Permanent Magnet Generators possess a multitude of
attractive features such as better design flexibility, higher power
to weight ratio, negligible cogging torque, lower noise, adjustable
planar air gap, higher energy efficiency, possibility of modular construction etc. They can be designed in a wide variety of topologies
having multiple stators and rotors in the same machine with different assemblies for stator winding and different configurations
for the placement of permanent magnets [17–21]. Axial Flux Permanent Magnet Generators can also be designed with several
stages of stator-rotor units mechanically coupled together on the
same shaft and electrically connected together in series or parallel
as required. By doing so, the electrical output that can be generated
from the available wind increases as many folds as generated by a
single stage, with minimal increase in overall size.
Among the various configurations, Single Stator Double Rotor
(SSDR) configuration is found to have better operational features
and in this configuration, the stator carrying three phase winding
115
Fig. 1. AFPMG with SSDR (NS-SN) configuration.
116
S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124
3 Iph Zph
p Dso 2þDsi
ac ¼
ð2Þ
where Iph is the stator phase current, Zph is the number of stator
conductors per phase.
Voltage induced by the permanent magnet poles on the stator
conductors is given by,
Vph ¼ Ke Ns
ð3Þ
where Ke is the induced emf constant in given by the following
relation,
p
Ke ¼
4
Zph Bav ðD2so D2si Þ
ð4Þ
Number of turns per phase in stator,
Tph
Zph
ðDso þ Dsi Þ
¼
¼ ac p 2 6 Iph
2
Iph
J
ð5Þ
ð6Þ
Length of Mean Turn in mm,
Lmt ¼ ðDso Dsi Þ 103 þ Loht þ Lohb
Ld ¼
l0 T2ph p D2so D2si
4
0:8 þ Lg 2 þ Lsb
ð17Þ
Quadrature axis inductance,
Lq ¼
l0 T2ph p ðD2so D2si Þ
ð18Þ
4 fðLp þ 0:8 þ Lg Þ 2 þ Lsb g
Direct axis reactance,
Xd ¼ 2 p f Ld
ð19Þ
Quadrature axis reactance,
For a current density of J (chosen as 4.1 A/mm2), the area of
conductor,
as ¼
where Lp is the thickness of pole (taken as 12.5 mm), Lg is the air
gap length (taken as 1 mm) and Lsb is the bottom thickness of the
stator.Direct axis inductance,
Xq ¼ 2 p f Lq
ð20Þ
For this particular design of AFPMG, the iron losses are absent,
copper losses are present in stator winding only and neglecting the
mechanical losses, the efficiency equation can be written as
g¼
Pout cos £ 100
ðPout cos £Þ þ pscu
ð21Þ
where cos £ is the power factor.
ð7Þ
where Loht and Lohb are top and bottom overhangs of the stator
winding. The other coil dimensions are worked out as per standard
designing procedure.
The stator resistance per phase at 20 °C and 75 °C is given by,
Rph20 ¼
1:732
108 Lmt Tph 1:08
as
ð8Þ
Rph75 ¼
1:3
Rph20
1:08
ð9Þ
Design output
The SSDR AFPMG is rated at 2000 VA, 240 V(phase), 10 pole, 3
phase, 25 Hz, 5 rps and its design output has been listed in Table 1.
Higher specific magnetic and electric loadings are chosen so that
the machine has reduced volume and size. The diameter ratio, k,
is an influencing parameter in the design of AFPMG as the copper
losses depends on this factor [25]. Hence an optimized value has
been chosen for k as 0.23 for this design to maximise the efficiency
of AFPMG.
Stator copper loss,
pscu ¼ 3 I2ph Rph75
ð10Þ
For P number of Poles on each rotor disc, Pole Pitch Top and Pole
Pitch Bottom is given by,
p
p
st ¼ Dso and sb ¼ Dsi respectively:
P
P
ð11Þ
Flux per Pole in the rotor,
p
£p ¼
4P
ðD2so D2si Þ Bav
ð12Þ
Thickness of rotor end plate,
Lrep ¼
£p 103
Bmax ðDso Dsi Þ
ð13Þ
where Bmax is the maximum flux density in the rotor end plate
which is assumed as 1.55 Wb/m2.Electromagnetic torque,
C¼
Pout 103
2 p Ns
ð14Þ
Shaft Diameter,
Dshaft
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4C
3
¼
p rmax
ð15Þ
where rmax is the maximum permissible shear stress
Length of machine,
L ¼ ½ðLp þ 0:8 þ Lg Þ 2 þ Lsb þ 2 Lrep ð16Þ
Table 1
Design Output for 2000 VA, 240 V, 3 phase, 10 pole, 25 Hz AFPMG.
Parameter
Symbol
Value
Unit
Generator output
Frequency
Rated phase voltage
No. of phases
Rated Speed
No. of poles
Average flux density in air gap
Specific Electric Loading
Diameter ratio
Outer diameter of stator
Inner diameter of stator
Induced emf constant
Number of conductors per phase
Area of Conductor
Length of mean turn
Stator Resistance per phase at 75 °C
Thickness of pole
Height of pole
Pole Pitch Top
Pole Pitch Bottom
Pole Arc to Pole Pitch Ratio
Pole Arc Top
Pole Arc Bottom
Electromagnetic torque
Shaft diameter
Length of machine
Direct Axis Inductance
Quadrature Axis Inductance
Stator Copper Loss
Efficiency
Pout
f
Vph
Phase
Ns
P
Bav
Ac
k
Dso
Dsi
Ke
Zph
as
Lmt
Rph75
Lp
Hp
2000
25
240
3
5
10
0.6
17666
0.23
0.301
0.069
50.16
1240
0.811
0.43
7.39
12.5
116
94.56
21.67
0.7
66.2
15.18
63.661
21.11
0.696
0.247
0.066
170.6
92.14
VA
Hz
V
–
rps
–
Wb/m2
A-cond/m
–
m
m
V/rps
–
mm2
m
O
mm
mm
mm
mm
–
mm
mm
Nm
mm
m
H
H
W
%
st
sb
–
–
–
C
Dshaft
L
Ld
Lq
pscu
g
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117
Modeling of Axial Flux Permanent Magnet Wind Generator
The direct drive variable speed system under consideration consists of SSDR AFPMG directly coupled to a Horizontal Axis Wind
Turbine (HAWT) without any gear box using a simple shaft. The
auxiliary components of this system include speed controller and
pitch controller. The focus of this study is on the dynamic modeling
and simulation of the AFPMG operated as a wind generator to
understand its response under different wind conditions using
MATLAB/Simulink platform. The development of the model for
each component has been presented below.
Model of HAWT
A conventional three bladed HAWT is considered for the analysis and its mathematical modeling equations have been given
below [11–13].
Mechanical Power generated by turbine,
Pm ¼
1
Cp q A U3w
2
Fig. 2. Power Coefficient (Cp ) vs. Tip Speed Ratio (k) for different values of Pitch
angle (b).
ð22Þ
where q is the air density (taken as 1.225 kg/m3 at normal temperature), A is the area swept by the turbine blades (in m2), Uw is the
upstream wind speed (in m/s) and Cp is the power coefficient.
Power coefficient ðCp ) is the ratio of mechanical power generated by the turbine to the power available in the wind. It is a
non-linear function of tip speed ratio (k) and pitch angle of the
blades (b). The theoretical maximum value of Cp is 0.59 (limited
by Betz criterion) while practical values lie between 0.4 and 0.45.
Although many variations of the equation for power coefficient
exists, a standard equation has been used here as follows.
Cp ¼ C1
C
C2
5
C3 b C4 e ki þ C6 k
ki
ð23Þ
The coefficients are taken as: C1 = 0.5176, C2 = 116, C3 = 0.4,
C4 = 5, C5 = 21 and C6 = 0.0068
Tip Speed Ratio,
k¼
xm R
Uw
ð24Þ
Model of AFPMG
where xm is the blade tip speed, which is equal to the rotor angular
speed (in rad/s) and R is the radius of the turbine rotor.
ki ¼
1
0:035
k þ 0:08b b3 þ 1
ð25Þ
Mechanical torque developed by turbine,
Tm ¼
Pm
xm
Fig. 3. Mechanical Power ðPm Þ vs. Angular Speed ðxm Þ for different Wind speeds
ðUw Þ.
ð26Þ
The variation of power coefficient Cp with respect to tip speed
ratio k for different values of pitch angle b is shown in Fig. 2. As
seen from the figure, the power coefficient decreases as pitch angle
is increased for the same tip speed ratio. From the equation for tip
speed ratio, it is clear that there exists an optimal value for k for
every wind speed Uw . The value of xm corresponding to this k is
considered to be optimum for extracting the maximum power
from the particular wind speed. The variation of power developed
by the turbine with respect to the variation in angular rotational
speed for different wind speeds has been shown in Fig. 3.
A MATLAB/Simulink model for the wind turbine has been developed using the above modeling equations as shown in Fig. 4.
The dynamic model of AFPMG is developed using synchronous
d-q rotating reference frame on the lines of Permanent Magnet
Synchronous Generator [7,13,26,27]. In this frame it is considered
that the q-axis is 90° ahead of d-axis. The transformation of the
three phase system to d-q frame is maintained by Park’s transformation and the reverse transformation by Inverse Park’s Transformation as given below.
2
3
2
32 3
cos xt
cosðxt 120Þ
cosðxt þ 120Þ
ua
ud
6 7 2 6 sin xt sinðxt 120Þ sinðxt þ 120Þ 76 7
4 uq 5 ¼ 4
5 4 ub 5
3
1
1
1
u0
uc
2
2
2
2
3 2
32 3
ud
ua
cos xt
sin xt
1
6 7 6
76 7
4 ub 5 ¼ 4 cosðxt 120Þ sinðxt 120Þ 1 54 uq 5
uc
u0
cosðxt þ 120Þ sinðxt þ 120Þ 1
where ‘u’ can be voltage, current or flux.
The modeling equations of AFPMG have been developed by
assuming that the rotor flux completely acts along d-axis and there
is no flux along q-axis.
Flux linkages along d and q axes are given by
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S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124
Fig. 4. MATLAB/Simulink model of Horizontal Axis Wind Turbine.
wd ¼ Ld id þ wf
ð27Þ
wq ¼ Lq iq
ð28Þ
where Ld and Lq are inductances along d and q axes respectively, id
and iq are the stator currents along d and q axes respectively. wf is
the permanent magnet flux linkage given by
wf ¼
Ke
pP
ð29Þ
Pe ¼
3
ðxe Lq iq id xe Ld id iq þ xe wf iq Þ
2
or,
Pe ¼
3
xe ½wf iq ðLd Lq Þid iq 2
ð38Þ
The electromagnetic torque developed is given by
Te ¼
Pe
xm
¼
P 3
½w iq ðLd Lq Þid iq 2 2 f
ð39Þ
where Ke is the induced emf constant of the AFPMG and P is the
number of poles.
The voltage equations along d and q axes are given by
The MATLAB/Simulink model of the AFPMG developed based on
the above modeling equations has been shown in Figs. 5–7.
vd ¼ rd id þ pwd xe wq
ð30Þ
Model of drive train
vq ¼ rq iq þ p wq þ xe wd
ð31Þ
where rd and rq are the resistances of the stator in d and q axes, xe is
the angular electrical speed and p represents d=dt.
Substituting the values of wd and wq from Eq. (27) and (28), we
get
vd ¼ rd id Ld pid þ xe Lq iq
ð32Þ
vq ¼ rq iq Lq piq xe Ld id þ xe wf
ð33Þ
Rearranging Eqs. (30) and (31), the current equations can be
obtained as
did
1
¼ ½rd id þ xe Lq iq vd dt Ld
ð34Þ
diq
1
¼ ½rq iq xe Ld id þ xe wf vq dt Lq
ð35Þ
The drive train represents the mechanical connection between
the wind turbine and generator and its mathematical expression
is given by the Swing equation. It characterizes the behaviour of
rotor of the generator with respect to the input mechanical torque
and output electromagnetic torque. The wind turbine and AFPMG
are coupled directly through a shaft and therefore a simple lumped
mass model has been considered [7,13] and the differential equation which represent the drive train is given by
J
dxm
¼ T m T e Kx m
dt
where J is the moment of inertia of rotor mass, xm is the angular
velocity of turbine shaft (angular mechanical speed), Tm is the
mechanical torque developed by turbine, Te is the electromagnetic
torque developed by generator and K is the friction coefficient.
The MATLAB/Simulink model of the drive train has been shown
in Fig. 8.
The relation between electrical rotating speed and mechanical
speed is given by
xe ¼ xm P
2
ð36Þ
The electromagnetic power generated by the AFPMG is given by
Pe ¼
3
ðed id þ eq iq Þ
2
ð37Þ
where ed and eq are induced emfs in d and q axes given by
ed ¼ xe Lq iq and eq ¼ xe Ld id þ xe wf
Substituting the expressions for ed and eq in Eq. (35)
ð40Þ
Fig. 5. MATLAB/Simulink model of AFPMG – Computation of vd .
S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124
119
the current wind speed and the controller generates a iq control signal which is given as feedback to the AFPMG block for torque and
voltage build up. The speed controller is designed in such a way that
system settles down at the appropriate operating point with respect
to available wind speed. The d-axis component of current is set to
zero to maximise the torque development at the rated flux and minimize the losses.
The MATLAB/Simulink model of the speed controller is shown
in Fig. 9.
Pitch controller
Fig. 6. MATLAB/Simulink model of AFPMG – Computation of vq .
Speed controller
The wind speed being a highly variable input, it becomes necessary that the speed of the rotation of the generator and in turn the
speed of the turbine has to be adjusted so that the system speed is
brought to the optimal value where maximum power extraction
from the wind and hence maximum power generation by the
AFPMG would be possible. Field oriented vector control approach
is one of the methods by which this is achieved, where the qaxis component of the stator current is the controlling factor
[12,26,28]. It is clear from Eq. (37) that electromagnetic torque is
dependent on q-axis current, hence if iq is controlled, then Te can
be controlled. By controlling toque, the shaft speed xm , can be controlled as seen from Eq. (38). A speed controller incorporating the
elements of this control approach has been adopted in this paper
with a purpose to simulate the effect of both maximum power
point tracking operation and loading effect on the AFPMG. It is
designed based on a forcing function given by
iq ¼ A Dx ð1 e
t=Tc
Þ
As the wind speed increases, the speed of rotation of the wind
turbine will naturally increase, causing the generator to run at
speeds higher than its nominal speed and generate overvoltage.
To prevent this and to keep the power within the designed limits,
the turbine torque needs to be controlled when the generator
speed exceeds its limit. From Eq. (23), it is clear that pitch angle
of the turbine blades (b) can be adjusted to control the power coef-
ð41Þ
where A is a constant, Dx is the speed error, i.e., the difference
between actual speed and reference speed, Tc is the time constant.
A is chosen as 80 and Tc is chosen as 300 to minimize fluctuations
and ensure smooth settling. Reference speed is generated based on
Fig. 9. MATLAB/Simulink model of Speed Controller.
Fig. 7. MATLAB/Simulink model of AFPMG – Computation of Te and Pe .
Fig. 8. MATLAB/Simulink model of Drive Train.
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S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124
ficient and in turn, control the turbine power output and torque.
For the wind speeds lower than or equal to the nominal speed,
the pitch angle of the blades is kept at 0° to extract as much power
as possible from the wind. During this period, the action of speed
controller alone takes care of the optimal speed at which the system operates. As wind speed exceeds the limit corresponding to
the nominal speed of the generator, pitch controller is activated
and the pitch angle is increased progressively to limit the speed
and to keep the output power on or below the rated value. b is usually varied between 0° and 24° for pitch control in this mode. Once
the wind speed reaches the cut-off limit, the pitch angle is set to
90° so that the wind turbine comes to a halt in order to avoid
mechanical failure.
The pitch angle is calculated based on an error signal which is
the difference between the electromagnetic power and the rated
power (reference signal) [26–28]. It employs a proportional (P)
controller to process the error signal. This methodology for pitch
control has been implemented using MATLAB/Simulink platform
as shown in Fig. 10. A selector switch is used to select the state
of operation according to the wind speed control input. The rate
of change pitch angle is limited to 3° per second to minimize stress
on the blades and disturbances in the speed of rotation.
The MATLAB/Simulink model of the complete system is shown
in Fig. 11.
Table 2
Parameters used for Simulation.
Parameter
Symbol
Value
Unit
Rotor Diameter of Wind Turbine
Air density
Number of poles in AFPMG
d-Axis component of stator resistance
q-Axis component of stator resistance
d-Axis component of stator inductance
q-Axis component of stator inductance
Permanent magnet flux linkage
Power Reference
Moment of Inertia
Friction coefficient
D
Rho
P
Rd
Rq
Ld
Lq
Psi
Pref
J
K
4
1.225
10
5
5
0.247
0.066
1.6
2000
4
0.16
m
kg/m3
–
Fig. 10. MATLAB/Simulink model of Pitch Controller.
Fig. 11. Complete MATLAB/Simulink model of the AFPMG based wind generator.
X
X
H
H
Wb-turns
VA
kg m2
Nm/rad
S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124
Parameters used for simulation
The parameters used for the simulation of wind turbine driven 3 phase, 240 V, 25 Hz, 5 rps AFPMG with a rated power of
2000 VA and electromagnetic torque of 66 Nm is listed in Table 2
along with their corresponding symbols used in the MATLAB/
Simulink blocks. The cut-in and cut-off wind speed of the pitch
121
variable three bladed HAWT is designed to be 4 m/s and 15 m/
s respectively.
Results and discussion
The operation of the complete system has been simulated for
various wind conditions, comprising of constant wind speed, a
Fig. 12. Variation of a) Mechanical Speed ðxm Þ, b) frequency ðfÞ, c) Electromagnetic Torque ðTe Þ and d) Electromagnetic Power ðPe Þ for various constant wind speeds ðUw Þ.
Fig. 13. Variation of a) Mechanical Torque ðTm Þ, b) Mechanical Power ðPm Þ, c) q-axis current (iq ), d) frequency ðfÞ for nominal wind speed of 8.5 m/s.
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rapidly varying wind speed and high wind speed input, to evaluate
the dynamic behaviour of the wind generator.
Constant wind speed response
Fig. 12 shows the values of mechanical speed, electromagnetic
power, electromagnetic torque and frequency for constant wind
speeds of 6, 7, 8 and 8.5 m/s. It can be observed that for these wind
speeds, the speed controller assists the system to settle down at
the suitable speed and the operation of the turbine and AFPMG is
such that the maximum possible power is generated at each wind
speed. Also, it is clear that the generator operates at its rated values
i.e., power of 2000 VA and voltage of 240 V at speed of 5 rps (i.e.,
31.4 rad/s or 300 rpm) when the wind speed is 8.5 m/s which is
the nominal wind speed.
The mechanical torque, mechanical power, q-axis current and
the frequency at the nominal wind speed of 8.5 m/s have been
shown in Fig. 13. The d and q-axes components of stator voltages
and the three phase voltage output for this wind speeds have been
shown in Fig. 14. For the three phase output voltage, a section has
been expanded and shown to elucidate the balanced three phase
nature of the three phase voltages.
ative steps of wind speeds. The variations in electromagnetic
power and the three phase output voltage of the generator with
respect to the random wind pattern has also been shown in the figure. It can be seen that the generator is able to quickly adapt to the
changing wind conditions and the transients are quite short in
nature.
High wind speed response
As discussed previously, at wind speeds higher than the nominal value, the pitch control is activated. In order to clearly demonstrate the action of pitch controller, a three stepped wind pattern
has been chosen with speeds 8.5 m/s, 10 m/s and 11 m/s as shown
in the Fig. 16. The variation of the pitch angle, angular mechanical
speed and electromagnetic power with respect to the change in
wind speed also has been shown the figure. For the first 20 s, the
wind speed remains at 8.5 m/s which is the rated wind speed. During this time pitch angle is set to 0° to extract maximum power
from the wind. For the next 10 s, the wind speed increases to
10 m/s and then the pitch controller is activated. It is seen that
Variable wind speed response
To understand the dynamic response of the generator, its operation has been simulated for a rapidly varying wind pattern as
shown in Fig. 15. This wind pattern includes both positive and neg-
Fig. 14. a) d and q axis voltages ðVd ; Vq Þ, b) Three phase output voltage ðVa ; Vb ; Vc Þ
for wind speed of 8.5 m/s.
Fig. 15. Variation of a) Wind speed ðUw Þ, b) Electromagnetic Power ðPe Þ, c) Three
phase output voltage ðVa ; Vb ; Vc Þ with respect to time.
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Fig. 16. Variation of a) Wind Speed ðUw Þ, b) Pitch angle ðbÞ, c) Angular Speed ðxm Þ, d) Electromagnetic Power ðPe Þ at high wind speed conditions.
the pitch angle increases to 2.8° due to which the turbine is prevented from further acceleration and the mechanical speed
remains well within the rated speed. The power generated by the
AFPMG also remains close to the rated power. Again for the next
10 s, when the wind speed increases to 11 m/s, the pitch angle
becomes 7.2°. Similar effects can be seen on the speed and power
during this time as well. The output voltage would also remain limited at the rated value during active pitch operation. Evidently, the
pitch controller is successfully able to control the power of the
AFPMG at high wind speed conditions.
Table 3
Validation Chart.
Wind
Speed
Parameter
Calculated Result
Simulated Result
7 m/s
Tip Speed Ratio
Angular Mechanical
Speed
Power Coefficient
Turbine Power
Angular Electrical
Speed
Frequency
Electromagnetic
Power
q-Axis current
Per phase output
voltage
8
28 rad/s or
267.5 rpm
0.47
1240 W
140 rad/s
8.1
28.35 rad/s or
270.85 rpm
0.46
1213 W
141.75 rad/s
22.3 Hz
1142 VA
22.57 Hz
1173.7 VA
3.4 A
208 V
3.45
212.4 V
Tip Speed Ratio
Angular Mechanical
Speed
Power Coefficient
Turbine Power
Angular Electrical
Speed
Frequency
Electromagnetic
Power
q-Axis current
Per phase output
voltage
7.4
31.4 rad/s or
300 rpm
0.462
2183 W
157 rad/s
7.45
31.66 rad/s or
302.4 rpm
0.463
2188.2
158.6 rad/s
25 Hz
2000 VA
25.25 Hz
2036.4 VA
5.3 A
240 V
5.35 A
242 V
Validation of the model
The simulation results presented above prove that the proposed
model satisfactorily captures the real-time behaviour of the wind
generator and mimics the system dynamics. The results of simulation have been verified against calculated results to further establish the validity of the developed model. It is to be noted that the
only independent input to the whole system is wind speed, hence
validation has been performed for two wind speeds, i.e. rated
speed of 8.5 m/s and another token wind speed of 7 m/s. The
expected results have been calculated using the formulae associated with the various components of the system whereas the simulated results have been obtained from the simulations of the
MATLAB/Simulink model (also illustrated using the graphs and
plots given above). Tip speed ratio for the particular wind speed
has been estimated from the wind turbine characteristic plots.
Comparison of simulation results with theoretical results have
been shown in Table 3.
The design data for the 2000 VA, 240 V AFPMG was fed to the
model and, in turn, from the simulation results it has been shown
that the model is able to successfully reproduce the generator output for its entire operational speed range. The validation chart
shows that the simulated results match the estimated results with
acceptable tolerance which validates the model.
Conclusion
An AFPMG has been designed considering SSDR structure with
NS-SN pole configuration, suitable for variable speed wind energy
systems and its basic design equations have been presented. This
8.5 m/s
configuration has been found to have structural and functional
advantages including zero iron losses, lighter weight and compact
structure. The design output for the AFPMG rated at 2000 VA,
240 V, 10 pole, 3 phase 25 Hz, 5 rps is also listed. The mathematical
model of the direct driven AFPMG along with the models developed for the HAWT, drive train, speed controller and pitch controller have also been presented. The detailed MATLAB/Simulink
model implemented for each component has also been given. Simulations were carried out on the model for various wind conditions
and the corresponding behaviour and response of the wind generator was analysed. It has been observed that the wind generator
responds quickly to the varying wind conditions adapting to the
optimal operating speed as per the available wind speed and performs satisfactorily in all cases. The action of pitch controller and
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its effect on power control at high wind speeds has also been successfully demonstrated. From the simulation analysis, it can be
safely concluded that AFPMG with SSDR (NS-SN) configuration is
one of the best options for variable speed wind energy conversion
systems.
Acknowledgements
I am deeply obliged to my co-authors for their valuable support
in the research work and preparation of this paper. I wish to extend
my sincere thanks to my colleagues who proof read this manuscript and gave inputs to improve the presentation. The research
work covered in this paper has not been funded by any sources
and any expense incurred has been borne by myself.
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