Energy and Power Engineering, 2013, 5, 423-428
doi:10.4236/epe.2013.54B082 Published Online July 2013 (http://www.scirp.org/journal/epe)
Performance analysis of 20 Pole 1.5 KW Three Phase
Permanent Magnet Synchronous Generator for low Speed
Vertical Axis Wind Turbine*
Shahrukh Adnan Khan1, Rajprasad K. Rajkumar1, Rajparthiban K. Rajkumar1, Aravind CV2
1Faculty of Engineering, University of Nottingham Malaysia Campus, Jalan Broga, Semenyih, Malaysia
2School of Engineering, Taylor’s University, Selangor, Malaysia
[e-mail] [e-mail]
Received April, 2013
ABSTRACT
This paper gives performance analysis of a three phase Permanent Magnet Synchronous Generator (PMSG) connected
to a Vertical Axis Wind Turbine (VAWT). Low speed wind condition (less than 5 m/s) is taken in consideration and the
entire simulation is carried in Matlab/Simulink environment. The rated power for the generator is fixed at 1.5 KW and
number of pole at 20. It is observed under low wind speed of 6 m/s, a turbine having approximately 1 m of radius and
2.6 m of height develops 150 Nm mechanical torque that can generate power up to 1.5 KW. The generator is designed
using modeling tool and is fabricated. The fabricated generator is tested in the laboratory with the simulation result for
the error analysis. The range of error is about 5%-27% for the same output power value. The limitations and possible
causes for error are presented and discussed.
Keywords: Vertical Axis Wind Turbine; Three Phase Multi-pole permanent Magnet Synchronous Generator; Low
Wind Speed; Modeling; Performance Analysis
1. Introduction
Various countries worldwide are aware of the fact that
the past and current trends of energy system are not sus-
tainable and a solution needs to be drawn to secure the
world energy from a drastic falling. One of the sources
that can replace the current trend is surely wind energy
which greatly depends on the availability of the wind
resource. Areas found around the equatorial regions tend
to have low wind speeds. For example, Malaysia cur-
rently has an average wind speed of 2-3 m/s, with higher
wind velocity in the east coast of west Malaysia [1]. For
a typical horizontal axis wind turbine to run and generate
power, a wind speed of at least 5 m/s is required [2]. A
speed that is less than 5 m/s is not sufficient to turn the
turbine. Another predicament is that these regions face
unsteady multi-directional winds making HAWT totally
incompatible in such areas. The vertical axis wind tur-
bine (VAWT) on the other hand is appropriate for such
regions due to its ability to capture wind energy at any
direction. Also, the use neodymium magnets for suspen-
sion at the bottom surface assist attaining zero friction,
which helps counter the low wind speed problem [2].
Conventional generators can be replaced with Perma-
nent Magnet Synchronous Generator (PMSG) using multi-
pole stator arrangement. The multi-pole stator arrange-
ment can be configured to generate high voltage at low
revolution, and high current at faster speeds. The stator is
designed to produce negligible cogging torque therefore
causing the generator to start up and cut-in at low speeds
to produce high current [3]. One significant advantage of
PMSG, is that it is much lighter, smaller in size, and uses
less constructional material so lowering cost and hub size
[2][3]. Although a number of researches in the area of
VAWT and PMSG are carried through separately, few
attempts were taken to build a system together that work
more efficiently at low wind speed. Moreover, there is a
significant lack of research to find an optimal multi-pole
PMSG for a VAWT with a fixed swept area which is
realistic to work in those low wind speed countries.
The main objective of this paper is to simulate and inves-
tigate the response of a permanent synchronous generator
of a vertical wind turbine under different operating sce-
nario through in Matlab/ Simulink environment.
2. Methodology
The equations of VAWT and PMSG are implemented in
SIMULINK and a graphical user interface is developed
to aid users in designing the VAWT. For the modeling

S. A. KHAN ET AL.
424
part, at first the turbine section is designed. The radius,
wind speed, the swept area, the power coefficients and
pitch angles are made as variables. After designing the
turbine, simulation is performed and the data is compared
with the analytical design value to ensure the accuracy of
the turbine design. Later, with the changing parameters,
the torque and the power output values are observed and
optimal design parameters are derived. The simulation of
PMSG is carried for different values of mechanical
torque and speed for the pre selected values from the
simulation and lastly the load voltage, current and power
are measured for evaluation. The generator design is de-
veloped and is experimentally tested and compared with
the simulation data. Figure 1 show the methodology
used in this approach.
3. Modelling
3.1. Design of VAWT
The design of VAWT derived from the work stated in
[5-12].
The aerodynamic power Pm of the turbine is given by
the Equation 1.
Pm = Cp (λ) U
w
3 (1)
Here, is the air density in (kg/m3) at normal tem-
perature, A is the area covered by the wind turbine rotor
in (m2), Uw is the wind speed in (ms-1), Cp is the power
coefficient of the wind turbine and is the tip-speed
ratio and is related to the rotor speed ( in rads-1) in as
in Equation 2.
λ = Cp (2)
(3)
where R is turbine radius in (m), H is the turbine height
in (m). The power coefficient Cp is given as a function of
ѳ (pitch angle of the turbine) and (the tip-speed ratio).
The value of Cp can only go as high as 0.59 according to
the Betz law [6, 7]. The mechanical torque is related with
mechanical power by Equation 4.
Figure 1. Methodology used in this design.
(4)
Figure 2 shows the modeling and design of the turbine.
For computation of the power coefficient, maximum
power coefficient is at null pitch angle is 0.4412 [1].
Taking the value of Cp as 0.4412, air density as 1.225,
the above mentioned equations are used to calculate the
swept area, mechanical power from the turbine and me-
chanical torque generated from it. Wind speed, radius
and the height of the turbines are varied in the simulation
to get optimal torque and power.
3.2. Design of the Three Phases PMSG
Axial Flux Permanent Magnet (AFPM) motor with its
magnetic flux propagating at an axial direction from the
magnets and are best suited for low wind speed [4-5]
[12]. In comparison to the transverse flux design the ax-
ial flux design offers high torque and power density.
Therefore the AFPM is considered for the development
of this research work. The entire simulation is designed
in terms of park transformation analysis that is a vector
representation of three phase ac circuit models into a dq
reference coordinates [10-13] as shown in Figure 3.
The park transform equation is given below:
= (5)
Here, f can be current, voltage or flux .
Figure 2. Modeling of turbine.
Figure 3. Park transform for generators.

S. A. KHAN ET AL.
425
Tdq0 is given by Equation 6 . Here, p is the number of poles [12]. The dq frame cur-
rent is mentioned as follows [13]:
=
(15)
(6) (16)
Figure 4 shows the equivalent circuit for dq axis
where as Figure 5 represents the block diagram of three
phase PMSG which is designed in Simulink.
Here, q is the angular position. The coupling element
between turbine and generator is described with Swing’s
equation which is stated at Equation 7 and Equation 8.
The electromagnetic torque for generator [12]:
J = (7) (()) (17)
= (8) The stator resistance is taken as 14 Ω; inductance of
both dq axes is used as 0.8 mH; flux linkage established
by magnet is 0.175 Wb and mass inertia is considered to
be 0.089 kg/m2. The design is for 10 pole pairs and the
friction factor is neglected. The rated power at load is
considered to be 1.4 KW. An AC-DC rectifier is con-
nected at the load terminal of the generator to convert the
voltage and current to DC value. The inside subsystem
part of the generator is given as in Figure 6. Table 1
gives the values of parameters used in the design. The
optimal parameter for the generator is used for numerical
analysis. Figure 7(a) show the design of the generator
Figure 7(b) shows the fabricated generator.
Here, J is the total moment of inertia of the rotor mass
in kgm2, Tm is the mechanical torque in Nm , Te is the
electrical torque output of the generator in Nm, We is the
mechanical speed of the rotor in (rpm) and θ is the angu-
lar position of the rotor in (rad). Voltage of PMSG in the
d-q axis is then expressed as in Equation 9 - Equation 10.
(9)
(10)
From the above assertions, the dynamic electrical
model is shown as in Equation 11 – Equation 13.
(11)
+ (12)
+ (13)
Here, Ld, Lq and Lds, Lqs are the inductances and leak-
age inductances (H) on the d axis and q axis respectively.
iq, id and Uq, Ud are the stator currents and voltages cor-
responding to the d-axis and q-axis. Ra is stator resistance
(Ω), λo is the magnetic flux linkage (Wb). Here,
Figure 4. Equivalent q-axis and d-axis representation.
(14)
Figure 5. Modeling in Matlab/Simulink (Generator Part I).

S. A. KHAN ET AL.
426
Figure 6. Subsystem (Generator Part II).
Table 1. Design Parameter.
Model Parameter Name Value
Air Density 1.225kg/m3
Pitch Angle 0
Power Coefficient 0.4412
Wind Speed 2m/s-7m/s
Turbine Height 1.6m-2.6m
VAWT
Turbine Radius 1.6m-2.6m
Stator Phase Resistance 14 ohm
Inductance (d,q) 0.8mH
Flux Linkage 0.175V.s
Inertia 0.089J
Pole Pair 10
Rated Power 1.5KW
PMSG
Nominal Frequency 50Hz
(a) Design Structure (b) Fabricated Model
Figure 7. PMSG at optimal values.
4. Results and Discussion
4.1. Case 1 (Simulation of Turbine)
In this part, simulation is performed to get torque and
power for different values of radius and height keeping
one parameter fixed at a time and compared with ana-
lytical values to verify the accuracy of design. Figure 8
shows the analytical and simulation comparison of me-
chanical torque for different swept areas while varying
the radius of the turbine. The height is fixed at 2m. As it
can be seen from Figure 7, analytical and simulation
results are much closer to each other. This proves that the
design of the turbine created in modeling is appropriate
to work with. After taking consideration of different val-
ues of turbine radius and height, it is observed from Fig-
ure 9 that at low wind speed, 0.8 m-1.2 m radius would
be suitable for producing higher output power. However,
the radius of the turbine is taken to be a fixed value of
1m. From Figure 10, it can be observed that the height
between 2 m to 2.8 m is suitable to produce better output
power. Therefore, the height of it is fixed at 2.6 m.
4.2. Case 2 (PMSG connected to VAWT)
The stator resistance, inductance at dq frame, flux link-
age, mass inertia and pole pairs are varied and a set of
realistic parameter values are fixed (given in Table 1) in
which the voltage and current were satisfactory to pro-
duce power. The power is increased with the increase in
the number of pole and for practical consideration the
12 3 4 5 6 7
0
2
4
6
8
10
12
Swept Area of VAW T (m
2
)
Mechanical Torque (Nm)
Mechanical T orque v s Swept Area
Analytical Value
Si mulated Val ue
Figure 8. Mechanical Torque- Swept Area curve.
1.6 1.8 22.2 2.4 2.6 2.83
0
10
20
30
40
50
60
Radius of VAW T ( m )
Mec hanic al Tor que generated fr om V AW T (N m )
Mechani cal Torque vs Ra dius
v= 2 m/s
v= 4 m/s
v= 6 m/s
hei g ht 2 m
Figure 9. Torque generated for different radius.

S. A. KHAN ET AL. 427
number of pole pair is fixed at 10. Figure 11 evolved by
changing the mechanical torque for different wind speed
and keeping the generator parameter fixed at optimal
value. The load power is measured to make sure that the
generator is able to produce adequate output power for a
range of torque at low wind speed.
4.3. Case 3 (Hardware Testing)
The developed generator is experimentally tested at la-
boratory and the results are compared with that of the
simulation value. Figure 12 - Figure 14 shows theoreti-
cal and experimental comparisons for a fixed wind speed
of 6 m/s. Wind speed is taken as high value in order to
investigate the difference in value accurately.
The experimental values are quite identical with simu-
lation indicating the accuracy of the simulation design.
The simulation power values for different speed and
mechanical torque are higher than experimental values.
This is due to power loss for friction factor as it is ne-
glected in the simulation.
1.6 1.8 22.22.42.6 2.83
0
10
20
30
40
50
60
70
80
90
100
Hei ght of VAWT (m)
M ec hanic al Tor que generat ed fr om V AW T (N m )
Mechanical Torque vs Height
v= 2 m/s
v= 4 m/s
v= 6 m/s
radius 1m
Figure 10. Torque generated for different heights.
020 40 6080100 120 140 160 180
0
500
1000
1500
2000
2500
Mechanical Tor que (Nm)
Load Power (W)
Power vs Torque
v= 7m/s
v= 6m/s
v= 5m/s
v= 4m/s
v= 3m/s
Figure 11. Graph of Power values at the load for different
mechanical torque.
020 40 60 80 100
0
50
100
150
200
250
300
350
400
Rot ational Speed (RPM )
Load Voltage (V=RM S)
Vol tage v s RPM
Si m ul ated Data
Generator Testing Data
Figure 12. Voltage- Rotational Speed (RPM) curve.
020 4060 80100
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Rot ational Sp eed (RPM)
Load Power (W)
Power v s RPM
Simul at ed Value
Generated Value
Figure 13. Power- Rotational Speed (RPM) curve.
020406080100 120 140 160 18
0
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Mechanical Torque (N m )
Load Pow er (W )
Power vs Torque
Simulated Data
Gener ator Tes ting Dat a
Figure 14. Power- Torque curve.
5. Conclusions
An optimal system is built for low level wind speed. The
VAWT simulation produces torque and power with an
estimated error of ion ranging from 0.05%-10% accord-
ing to Table 2. After running several stages of simulation,

S. A. KHAN ET AL.
428
the swept area is
Table 2. Error Estimation of VAWT.
Mechanical Torque [Nm]
Swept Area
[m2] Theoretical Simulation
Error
[%]
1.6 0.68 0.7 2.9
2.4 1.557 1.7 9.18
3.2 2.76 2.84 2.9
4 4.29 4.324 0.8
4.8 6.226 6.3 1.18
5.6 8.474 8.3 2.05
6.4 11.069 11.074 0.05
Table 3. Error Estimation of PMSG.
Load Power
MechanicalTorque(Nm) Simulation Experimental Error (%)
52 148 126 14.90
68.6 284 240 15.49
83.4 416 367 11.81
100.2 586 534 8.81
116.9 817 733 10.23
132.9 1004 956 4.79
149.2 1262 1209 4.19
165.8 1878 1500 20.13
fixed at 5.2 m2 having fixed the radius and height of the
turbine to 1 m and 2.6 m respectively. For the generator
part, the simulation data is gathered for different values
of torque from the turbine; the design is built in CFD and
sent to a manufacturing company. Upon arrival, the gen-
erator is tested and load voltage and power were meas-
ured for different set of values of RPM and Torque. As it
can be seen in Table 3, there were differences while cal-
culating the error (5%- 27%) for load power. It is due to
the friction factor and stator inductance difference. This
VAWT with PMSG can make a significant impact for
low level wind situation in which Malaysia and so many
other countries stand.
6. Acknowledgements
The project is funded by the Ministry of Higher Educa-
tion (MOHE) of Malaysia under the ERGS grant.
REFERENCES
[1] Zaharim, S. K. Najid, A. M. Razali and K. Sopian “Wind
Speed Analysis in the East Coast of Malaysia,” European
Journal of Scientific Research, Vol. 32, No. 2, 2009, pp.
208-215.
[2] R. Bharanikumar, A. C. Yazhini and N. Kumar, “Model-
ling and Simulation of Wind Turbine Driven Permanent
magnet Generator with New MPPT Algorithm,” Asian
Power electronics journal, Vol. 4, 2012.
[3] W. Fei and P. I. Luk, “A New Technique of Cogging
Torque Suppression in Direct-Drive Permanent-Magnet
Brushless Machines,” IEEE Transactions on Industry
Applications, Vol. 46, No.4, 2010, pp. 1332-1340.
doi:10.1109/TIA.2010.2049551
[4] P. C. Krause, O. Wasynczuk and S. D. Sudho. “Analysis
of Electric Machinery and Drive Systems,” Wiley & Sons,
2002. doi:10.1109/9780470544167
[5] C. V. Aravind, Rajparthiban, Rajprasad and Y. V. Wong
“A Novel Magnetic Levitation Assisted Vertical Axis
Wind Turbine- design and Procedure,” IEEE Colloquium
on Signal Processing and its Applications , Melacca, Ma-
laysia CSPA 2012
[6] J A.M. De Broe, S. Drouilllet and V. Oevorglan, “A Peak
power Tracker for Small Wind Turbines in Battery
Charging Applications,” IEEE Transactions on Energy
Conv., Vol. 14, No. 4, Dec. 1999, pp. 1630-1635.
doi:10.1109/60.815116
[7] J. D. M. Whaley, W. L. Soongand and N. Ertugrul, "In-
vestigation of Switched-Mode Rectifier for Control of
Small-Scale Wind Turbines," Intl’ Conference Proceed.
of IEEE-IAS Annual Meeting, Vol. 4, 2005, pp.
2849-2856.
[8] S. Belakehal, H. Benalla and A. Bentounsi, “Power
Maximization of Small Wind System using Permanent
magnet Synchronous Generator” Revue des energies Re-
nouvelables, Vol. 12, No. 2 ,2009, pp. 307-319.
[9] J. G. SIootweg, H. Pollnder and W. L. Kling, “Repre-
senting Wind Turbine Electrical Generating Systems in
Fundamental Frequency Simulations," IEEE Trans. En-
ergy Convr, Vol. 18, No. 4, Dec. 2003, pp. 516-524.
[10] A. G. Westlake, J. R. Bumby and E. Spooner, "Damping
the Power-angle Oscillations of a Permanent Magnet
Synchronous Generator with Particular to Wind Applica-
tions," Proc. Ekct. Power Appl., Vol. 143, No. 3,
May1996, pp. 269-280. doi:10.1049/ip-epa:19960285
[11] C. Busca, A. Stan, T. Stanciu and D. I. Stroe “Control of
Permanent Magnet Synchronous of Large Wind Tur-
bines,” Denmark : Departament of Energy Technology:
Aalborg University, November 2010, Industrial Elec-
tronics (ISIE), pp. 3871-3876.
[12] M. Yin, G. Y. Li, M. Zhou and C. Y. Zhao, "Modeling
of the Wind Turbine with a Permanent Magnet Synchro-
nous Generator for Integration," Power Engineering So-
ciety General Meeting, 2007, pp.1-6.
[13] K. Tan and S. Islam, "Optimum Control Strategies in
Energy Conversion of PMSG Wind Turbine System
without Mechanical Sensors," Energy Conversion, IEEE
Transactions on, Vol. 19, No. 2, June 2007, pp. 392- 399.
doi:10.1109/TEC.2004.827038