Performance analysis of 20 Pole 1.5 KW Three Phase Permanent Magnet Synchronous Generator for low Speed Vertical Axis Wind Turbine

doi:10.4236/epe.2013.54B082

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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

Email: kecx1msa@nottingham.edu.my, Rajprasad.Raj[email protected],

Rajparthiban.Rajkumar@nottingham.edu.my [email protected]

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

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

Swept Area of VAW T (m

)

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

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

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

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

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

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

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.

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