Design and Modeling of Low-Speed Axial Flux Permanent Magnet Generator for Wind Based Micro-Generation

SystemsDaniyal Ahmed*, Fazal Karim** and Aftab Ahmad**

*Centres of Excellence in Science & Applied Technologies (CESAT),H-11/4, Islamabad, Pakistan

daniyal.ahmed@uettaxila.edu.pk**Department of Electrical Engineering, University of Engineering & Technology,

Taxila, Punjab Province, Pakistankarim.npcc@yahoo.com

aftab.ahmad@uettaxila.edu.pk

Abstract - Pakistan is currently hit by severe energy crisis. In both its urban and rural areas, the shortfall of electricity is so intense that it can cause power shut-down for as long as ten hours a day. In order to cope with this situation, harnessing renewable energy resources is crucial. Therefore, in this work an efficient, low-speed gearless wind based micro-generation system is proposed. Such a system can exploit wind energy in urban and rural parts of the country and can convert it to electrical energy to meet daily domestic energy requirements. A 1.5 kW low speed direct driven axial flux permanent magnet (AFPM) generator is designed for this system using analytical techniques. The generator comprises of modular structure having non-ferromagnetic core and offers special features as light weight, low wind speed operation capability and low maintenance cost. Such features make it superior to the available types of energy systems such as those utilizing Induction Generators (IG) and Synchronous Generators (SG). The design is implemented using dynamic modeling in MATLAB (Simulink) and validated through performance comparison with available state-of-the-art wind energy system models.

Index Terms – Axial flux permanent magnet (AFPM), building augmented wind turbine (BAWT), coreless, direct-driven, micro-generation.

I. INTRODUCTION

The high dependability on oil and other fossil fuels by South Asian countries has developed a severe energy crisis in the region, especially Pakistan. The share of furnace oil and gas in total derated capacity of Pakistan is about 65 percent according to figures obtained from department of National Power Control Centre, Islamabad. Keeping in view the scarce indigenous fossil fuel resources, Pakistan needs to harness its abundant alternate energy resources like wind, solar, hydel and their hybrid forms [1]. The total wind power potential of the

country is 346 GW. In order to exploit this potential, Govt. of Pakistan is working on installing large-scale wind generation systems in different areas of Sindh [2].

Renewable energy based small-scale or micro-generation systems are being utilized in different countries for electricity production such as building mounted wind turbine systems, solar panels and mini hydro-generation plants [3]. In urban and rural areas of Pakistan, solar and hydel energy based micro-generation systems are being utilized to overcome the shortfall of electricity however electricity production using wind-based micro-generation systems is still in its early stages. Therefore the main focus of this research work is on wind based micro-generation systems.

Extensive work has been carried out in this area worldwide especially in Europe where different projects of small scale wind generation have been installed on buildings [4-5]. Different types of wind turbines currently being used in urban environment are ducted wind turbines [6] and building augmented wind turbines (BAWT) [7]. Populated urban areas generally have lower wind speeds as compared to those of open areas. However, it has been analyzed in Ref. [7] that in urban areas, the concentration effect of buildings and corresponding wind flows can increase the wind speed locally, resulting in increased energy yield in comparison to open areas. In [8], the authors have analyzed that the optimal value of energy production depends upon the installation point of the wind turbines in buildings . This is due to the fact that the distance between buildings significantly alters the highest wind speed occurrence position. There is no significant change in maximum value of wind speed in-between the buildings with change in height; however on roof tops, this value increases with increase in height.

Performance of wind based generation system mainly depends upon the type of generator coupled with wind turbine to generate electrical energy [9]. Therefore extensive work has been done so far in the field of generator design for such

51

2014 International Conference on Robotics and Emerging Allied Technologies in Engineering (iCREATE) Islamabad, Pakistan, April 22-24, 2014

978-1-4799-5132-1/14/$31.00 ©2014 IEEE

systems. The type of generator being used in the system varies depending upon the system power ratings, air dynamics and the location where it is to be installed like open area or urban environment. Most common type of generators used in large scale wind based generation systems installed in open area, are induction generators (IG), doubly fed induction generators (DFIG), electrically excited synchronous generators (EESG) and permanent magnet synchronous generators (PMSG) [9-11]. Features of these machines like fixed speed operation (in case of IG) and partially variable speed (in case of DFIG), low efficiency at lower wind speed and high weight due to gear system restrict usage usually to larger wind farms installed at open areas [12]. The issue of fixed speed has been addressed in EESG but most attractive generator currently being used for wind based generation systems is PMSG. This generator can be used both for small scale and large scale generation systems [13-17]. Its wide area of applications include battery charging applications, human power applications, marine current generation system, portable hand crank generating system, induction heating and defense usage [18-23]. PMSGs are further categorized into axial flux permanent magnet (AFPM) and radial flux permanent magnet (RFPM) generators. AFPM generator has an advantage over RFPM generator in terms of power density, low speed efficiency and volume [9]. Therefore, this paper presents the design and modeling of 1.5kW low-speed direct-driven AFPM generator with modular structure having non-ferromagnetic cores for application to wind based micro-generation systems. Fig. 1 shows configuration of the proposed BAWT system prepared using Trimble SketchUp software [24]. The design/model is validated through performance comparison with micro-generation systems incorporating IG, DFIG and EESG. The comparison is carried out through simulations using the software MATLAB (Simulink) [25].

Fig. 1 Proposed Wind Based Micro-Generation System for buildings;1 – BAWT, 2 – Shaft directly coupled to BAWT , 3 – Designed AFPM

Generator, 4 – Generator 3-phase Output, 5 – AC/ DC Power Electronic Converter, 6 – DC feed to Battery Bank, 7 – Battery Bank (Energy

Storage).

II. GENERATOR DESIGN

A. Topology In literature, the AFPM generator is categorized under different topologies based on its design. On the basis of its rotor/stator configuration, it is categorized as single/dual-stator and single/dual-rotor based single-stage or multi-stage (two or more modules) generator. It is further categorized as coreless or cored and slot-less or slotted generator depending on its material. The designed generator in this proposed research consists of a three-staged structure. The structure of each stage or module consists of single-rotor in-between twin-stators. The two stators in each stage have identical structure and are electrically connected in series. Furthermore, the three stages are then electrically connected in parallel increasing the overall electrical power output of the generator. Both the twin-stators and the single-rotor in each stage have non-ferromagnetic cores. The stators which are stationary part of the generator are fixed with the frame whereas the rotors that constitute the rotating part are attached to the shaft of the generator. Fig. 2 shows the 2D model of this design topology. The non-ferromagnetic three-staged structure reduces losses, stator/rotor axial attractive forces , cogging torque and the overall weight of the generator. Hence this design results in increased wind energy utilization and efficiency.

Fig. 2 Designed AFPM Generator 2D Model; 1 – Dotted envelop showing Single Stage/Module, 2 – Twin-Stators, 3 – Single-Rotor, 4 –

Shaft,5 – Bearing, 6 – Frame.

B. Rotor and Stator Design The stator core consists of non-ferromagnetic material (resin) in which the stator coil is embedded. This coil consists of 3-phase dual-layered toroidal winding. The rotor placed in-between the dual stators in each stage consists of circular non-ferromagnetic material (aluminium) based disc supporting the neodymium permanent magnets (sintered NdFeB with 0% Co having magnetic strength of 40 MGOe). The neodymium magnets on the rotor are arranged in such a way that the magnetic field vector of each piece makes an

1

2

3

4

5

6

1

2

4

3 5 7

Inside View (Nacelle)

Building Rooftop

6 6

52

angle of 90° with its neighboring pieces. This arrangement of magnets, called the Halbach Array [26], increases the magnetic flux density in the air-gap between the stator and rotor in comparison to the basic arrangement of magnets in typical permanent magnet machines where this angle is 0°. The increase in density is because the flux lines of each magnet reinforce each other in the air-gap whereas they cancel out each other’s effect on the side where the non-ferromagnetic core is present. This arrangement has been verified with the help of finite element analysis techniques by designing a part of the rotor in the Finite Element Method magnetic (FEMM) software [27] as shown in Fig. 3 and Fig. 4. The peak value of magnetic flux density in the air-gap depends on characteristics of the permanent magnets and increases exponentially with the increase in height of the magnets.

Fig. 3 Flux Distribution & Density Plot of NdFeB Magnets with 0° angle between flux-lines of adjacent pieces.

Fig. 4 Flux Distribution & Density Plot of NdFeB Magnets with 90°

angle between flux-lines of adjacent pieces. C. Design Equations The peak value of flux density Bpeak in the air-gap as a result of the arrangement of magnets mentioned above is:

62.830.9 1 magnethpeak remB B e . (1)

In (1), hmagnet is axial height of the magnets and Brem is the remanent magnetic flux density. The electro-motive force Einduce

induced in a single side of the dual-stator is: 0.4467induce pair magnet turn elecpE N .

In (2), ppair is the pole-pair number of a single stage, magnet

is the flux, Nturn is the coil-turns per phase per stator sideand elec is the angular-speed in electrical degrees. The electro-magnetic torque Telec and power Selec of a single stage of the generator is:

0.679elec p pair magnet turn pn pT N I . (3)

(2 )elec p induce pnS E I . (4) In (3) and (4), Ip is phase current in the winding of the single-stage stator and np is phase number. The sizing equations to calculate diameter of the generator are:

13

1,

,

1.204 stage nomo

rpm nom peak

PD

B. (5)

0.577i oD D . (6) In (5) and (6), Do is the outer diameter, Di is the inner diameter of the generator, Pstage1,nom is the nominal output power of a single stage and rpm,nom is the nominal mechanical speed of the generator. D. Design Parameters The parameters of single stage of the designed 1.5kW AFPM generator have been shown in Table I.

TABLE I DESIGN PARAMETERS OF 1.5KW AFPM GENERATOR (SINGLE STAGE)

Parameter Value UnitNominal power output 0.5 kW

Nominal mechanical speed of rotor 25 rpm2.618 rad/sec

Nominal line voltage (star connection) 435 VPhase number 3 -Resistance of stator 0.01 mΩInductance of stator 1.2 mHPole pairs number 120 -Pole pitch 0.05 mDimensions of permanent magnets

Axial height 0.0254 mAxial width 0.0191 m

Axial length 0.0191 mPeak flux density in air gap(calculated analytically and from FEMM)

1.041 T

Dimensions of GeneratorOuter diameter 0.285 mInner diameter 0.165 m

Average diameter 0.225 mElectromotive force (EMF) constant 0.302 V.secMoment of inertia 0.387 Kg.m2

III. PROPOSED SYSTEM MODEL

The complete wind based micro-generation system for a building, already shown in Fig. 1, consists of the designed 1.5kW AFPM generator directly coupled to the BAWT without any gearbox using a simple shaft. The output of the generator is converted to DC via AC/DC power electronic converter and then stored in a battery bank of the building. The mathematical models of the BAWT, its drive-train and the designed AFPM generator have been presented. The scope of this research work is the designing and modeling of 1.5 kW AFPM generator for BAWT only, therefore, the modeling of AC/DC converter has not been covered.

Magnetic Flux Vector Orientation (shown by arrows)

Magnetic Flux Vector Orientation (shown by arrows)

53

A. BAWT The site selected for the design and modeling of BAWT in Pakistan is Karachi that has a number of tall buildings where this micro-generation system can be installed. Moreover, the average wind speed available in Karachi is quite suitable for small-scale wind turbines. For validation of the designed system, 12 m/sec, 10 m/sec, 7 m/sec and 4 m/sec wind speeds have been selected as input to the system models. The BAWT chosen for the designed system is a three-bladed horizontal-axis wind turbine. The output mechanical power Po,turbine and output torque To,turbine of the BAWT being extracted from the wind Vw upstream to the blades is:

2 3, ,

12 4o turbine b turbine karachi p wP D C V . (7)

,,

o turbineo turbine

turbine

PT . (8)

In (7) and (8), Db,turbine is diameter of the turbine blades,karachi is air density at Karachi site, Cp is performance

coefficient and turbine is rotating speed of BAWT. The maximum value of Cp which can be obtained theoretically is 0.59 [28]. The air density at Karachi site can be calculated using:

-40 1.194 10 ( )karachi karachi buildingE E . (9)

In (9), o is the sea level air density (1.225 kg.m-3), Ekarachi

and Ebuilding are the elevation of Karachi site and building rooftop from sea level. For variable-speed wind turbines, Cp

depends on pitch angle and tip speed ratio of the blades.Cp according to variable-speed turbine characteristics of [29], can be calculated as:

18.42.2

0 0110 0.4 0.002 9.6 i

pi

C e . (10)

In (10),

30 0

1

1 0.030.02 1

i and ,

2turbine b turbine

w

DV

.

Equations (7) to (10) have been implemented in MATLAB (Simulink) to develop the model shown in Fig. 5.

Fig. 5 BAWT (1.5kW) Model.

The design parameters of 1.5kW BAWT are given in Table II.

TABLE IIPARAMETERS OF 1.5 KW BAWT

Parameter Value UnitNominal power output 1.5 kWNominal wind speed 12 m/secDiameter of turbine blades 4 mSite (Karachi) air density 1.2094 Kg/m3

Site (Karachi) elevation 11 mHeight of building 120 m

B. Drive Train The drive train model represents the transfer of wind energy extracted by the blades of the turbine to the generator in the form of torque and speed. A single-mass drive system has been used to model the BAWT micro-generation system in MATLAB (Simulink) as shown in Fig. 6.

Fig. 6 Drive-Train Model.

The dynamic equation used to implement the drive-train in Simulink is:

, ,=gens em gen o turbine s gen

dT T F

dtJ . (11)

In (11), Js is the moment of inertia of the BAWT including the AFPM generator, Fs is the friction factor of the complete system, Tem,gen is the electromagnetic generator torque and gen

is the mechanical rotational speed of the drive train. The friction factor of the system is close to zero since there is no use of gear-box in the system. The lumped mechanical parameters of the complete system are shown in Table III. The mechanical parameters for the designed BAWT have been analytically calculated using the variable-speed turbine characteristics of [29] and [30].

TABLE IIIDRIVE T RAIN PARAMETERS

Parameter Value UnitMoment of inertia of BAWT including AFPM generator (lumped)

10.176+0.387 Kg.m2

Friction factor of BAWT including AFPM generator (lumped) 0.001 N.m.sec

C. 1.5kW AFPM Generator The dynamic model of the designed 1.5kW AFPM generator consists of three identical sub-models each representing a single stage connected in parallel. The model has been implemented by transforming the three-phase system to synchronous or direct-quadrature-zero (dq0) reference frame system using Park’s transformation [31] as follows:

0dq s abckv v . (12)

54

2 23 3

2 2 2where, 3 3 3

1 1 12 2 2

elec elec elec

s elec elec eleck

Cos Cos Cos

Sin Sin Sin ,

and, elec elec dt .

In (12), θelec is the electrical angular displacement of the generator. Since the designed AFPM generator is electrically balanced, therefore, the zero-sequence quantities can be ignored. Moreover, EMF induced in d-axis of the dual-stator is zero since d-axis is always aligned with permanent magnet flux position. Hence, the dq-axis equations of a single stage of the generator implemented in MATLAB (Simulink), as shown in Fig. 7, in simplified form are:

1 1L L

1L

q sE elec q elec d q

s s s

d sd elec q d

s s

ddtddt

i RK i i v

Li R

i i vL

. (13)

In (13), dq and idq are the dq-axis voltages and currents ,KE is the EMF constant, Rs is stator resistance and Ls is the stator inductance of a single stage of the designed generator.In addition to the above, the electromagnetic generator torque Tem,gen has been implemented in MATLAB (Simulink), as shown in Fig.7, using the following equation:

, 0.453em gen pair qT p i . (14) The design parameters of single-stage of the designed AFPM generator have been given already in Table I.

IV. RESULTS AND DISCUSSION

In this section, simulation results and performance of the designed 1.5kW low-speed direct-driven AFPM generator directly coupled to the BAWT under different wind speeds have been shown using MATLAB (Simulink). The designed system dynamic model has been compared with similar 1.5kW BAWT systems utilizing available state-of-the-art generators. These generators include IG, DFIG and EESG whose standard models, available at [25] have been used for simulation work.The results reported in this work include comparison of the simulated output active and reactive power, angular mechanical speed, performance factor and efficiency of these standard generators with the designed AFPM generator. The studies are carried out under similar operating conditions using the same 1.5kW BAWT.

Fig. 7 Electrical model of single-stage AFPM generator.A. Designed Generator Performance in BAWT The designed generator has a nominal speed of 25rpm (2.618 rad/sec) as mentioned in Table 1 which makes it highly suitable for locations where wind speed is comparatively low such as rooftops of buildings. The simulation results of the generator mechanical speed and active power have been recorded and shown in Fig. 8 and Fig. 9. The wind speed in these simulations has been varied from a peak value of 12m/sec to a value of 4 m/sec. B. Designed Generator Performance Comparison The results of performance comparison of the designed generator with standard generator models with respect to changing wind speeds have been shown in Fig. 10 to Fig. 13. Percentage performance factor Pfactor (efficiency) of each generator, as shown in Fig. 13, has been defined as follows:

100actualfactor

nom

PP

P. (15)

In (15), Pactual and Pnom are the actual and nominal output powers of a generator at a given wind speed. Pnom for all the generators under study is 1.5kW. The maximum efficiency of each generator under rated operating conditions has been shown in Table IV. In this table, the efficiency of coreless-stator AFPM generator with iron-cored-rotor, designed by R. J. Wang et. al in [32], has also been mentioned for the purpose of validation of the proposed design.

55

Fig. 8 Mechanical rotational speed under variable wind speeds.

Fig. 9 Active power delivered under variable wind speeds.

Fig. 10 Mechanical rotational speed Vs Wind speed.

Fig. 11 Active power Vs Wind speed.

Fig. 12 Reactive power Vs Wind speed.

Fig. 13 Performance factor Vs Wind speed. TABLE IV

GENERATOR EFFICIENCIES UNDER RATER OPERATING CONDITIONS

Generator Operating Speed Efficiency (%)

Proposed coreless low-speed direct-driven AFPM generator Variable 96.0

Coreless-stator AFPM generator proposed in Ref. [32] Variable 95.7

EESG Variable 73.67

DFIG Partially variable 70.8

IG Fixed 61.48From the results shown in Fig. 10 to Fig. 13 and in

Table IV, it can be seen that at any wind speed the designed AFPM generator is operating at a very low angular speed with negligible losses, highest wind power utilization, maximum efficiency and no reactive power requirements from the building’s power system to which it is being connected. In addition to the above, the designed generator also has coreless stator and rotor with gearless wind turbine operation making it the lightest generator among all under study.

V. CONCLUSION

In this research work, the design of low-speed three-staged direct-driven coreless AFPM generator based BAWT micro-generation system is proposed. The simulated results after comparison of the designed AFPM generator BAWT model with existing state-of-the-art generators based BWAT models prove that the designed generator has a very low angular speed with negligible losses, highest wind power utilization, maximum efficiency at all wind speeds, no reactive power consumption, coreless structure, gearless operation and lighter weight making the designed AFPM generator, the most

Vw: 12 m/sec

Vw: 10 m/sec

Vw: 7 m/sec

Vw: 4 m/sec

Vw: 12 m/sec

Vw: 7 m/sec

Vw: 4 m/sec

Vw: 10 m/sec

56

suitable and highly feasible generator for small-scale wind energy conversion systems, especially BAWT based micro-generation systems.

ACKNOWLEDGMENT

The authors thank Mr. Rizwan Masood for his valuedcontribution in preparation of this manuscript.

REFERENCES

[1] M. H. Abbasi, S. Rahman, S. A. Khan, N. Ehsan and E. Mirza. (2011, June). Green energy solution for power crisis in Pakistan [Online]. Available: http://www.researchgate.net/publication/228309876.

[2] Alternative Energy Development Board, MOWP, Govt. Pakistan. Wind Energy in Pakistan [Online]. Available:http://www.aedb.org/wind.htm.

[3] Bahaj and P. James, "Urban energy generation: the added value of photovoltaics in social housing," Renewable and Sustainable Energy Reviews, vol. 11, no. 9, pp. 2121-2136, 2007.

[4] N. Mithraratne, "Roof-top wind turbines for microgeneration in urban houses in New Zealand," J. Energy and Buildings, vol. 41, no. 10, pp. 1013-1018, 2009.

[5] List of Small Wind Turbines Projects [Online]. Available: http://re.emsd.gov.hk/english/wind/small/small_ep.html.

[6] Grant, C. Johnstone and N. Kelly, "Urban wind energy conversion: The potential of ducted turbines," J. Renewable Energy, vol. 33, no. 6, pp. 1157-1163, 2008.

[7] L. Lu and K. Y. Ip, "Investigation on the feasibility and enhancement methods of wind power utilization in high-rise buildings of Hong Kong," J. Renewable and Sustainable Energy Reviews, vol. 13, no. 2, pp. 450-461, 2009.

[8] D. Ayhan and Ş. Sağlam, "A technical review of building-mounted wind power systems and a sample simulation model," J. Renewable and Sustainable Energy Reviews, vol. 16, no. 1, pp. 1040-1049, 2012.

[9] D. Ahmed and A. Ahmad, "An optimal design of coreless direct -drive axial flux permanent magnet generator for wind turbine," J.Physics: Conf. Ser., vol. 439, no. 012039, doi: 10.1088/1742-6596/439/1/012039, 2013.

[10] R. J. Vieira, A. M. Sharaf and A. Elgammal, "Design of self-excited induction generators for wind applications," in Int. Conf. Elect. and Comput. Eng. (CCECE), Niagara Falls, Canada, 2011, pp. 000195-000200.

[11] S. Muller, M. Deicke and R. W. De-Doncker, "Doubly fed induction generator systems for wind turbines," IEEE Ind. Appl. Mag., vol. 8, no. 3, pp. 26-33, 2002.

[12] H. Li and Z. Chen, "Overview of different wind generator systems and their comparisons," IET J. Renewable Power Generation , vol. 2, no. 2,pp. 123-138, 2008.

[13] L. Gyeong-Chan and J. Tae-Uk, "Design of dual structural axial flux permanent magnet generator for small wind turbine," in TENCON Spring Conf., Sydney, Australia, 2013, pp. 90-94.

[14] K. Latoufis, G. Messinis, P. Kotsampopoulos and N. Hatziargyriou, "Axial Flux Permanent Magnet Generator Design for Low Cost Manufacturing of Small Wind Turbines," Multi-Science J. Wind Eng., vol. 36, no 4, pp. 411-432, 2012.

[15] H. Vansompel, P. Sergeant and L. Dupré, “Optimization of an axial-flux permanent-magnet generator for a small wind energy application," in 5th Strategic Energy Forum: A CO2-Lean Energy

Society by 2050: Transition and Business Opportunities, Brussels, Belgium, May 2011.

[16] H. Kobayashi, Y. Doi, K. Miyata and T . Minowa, "Design of axial-flux permanent magnet coreless generator for the multi-megawatts wind turbines," EWEA Proc. Europe’s Wind Energy Conf., France, March 2009, pp. 1-9.

[17] B. Xia, M. J. Jin, J. X. Shen and A. G. Zhang, "Design and analysis of an air-cored axial flux permanent magnet generator for small wind power application," in Int. Conf. Sustainable Energy Technologies (ICSET), Kandy, 2010, pp. 1-5.

[18] M. Eid, M. Abdel-Salam and M. T . Abdel-Rahman, "Vertical-axis wind turbine modeling and performance with axial-flux permanent magnet synchronous generator for battery charging applications," in Int. Conf. Power Syst. (MEPCON), El-Minia, Egypt, 2006, pp. 162-166.

[19] S. Ani, H. Polinder, J. Lee, S. Moon and D. Koo, "Performance of axial flux permanent magnet generator for human power application," in Int. IET Conf. Power Electron. Mach. Drives (PEMD), Bristol, 2012, pp. 1-5.

[20] Safari Doust and A. Rezaey, "A brushless axial flux permanent magnet generator with two mechanical powers inputs for marine current energy generation," Textboard J. Basic Appl. Sci. (JBASR), vol. 6, no. 5, pp. 6201-6209, 2012.

[21] J. Y. Lee, D. H. Koo, S. R. Moon and C. K. Han, “Design of an axial flux permanent magnet generator for a portable hand crank generating system,” IEEE Trans. Magn., vol. 48, no. 11, pp. 2977-2980, 2012.

[22] F. Caricchi, F. Maradei, G. De Donato and F. G. Capponi, “Axial-flux permanent-magnet generator for induction heating gensets,” IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 128-137, 2010.

[23] V. Parlikar, P. Kurulkar, K. Rathod and P. Kumari, "An axial-flux permanent magnet (AFPM) generator for defence applications-paradigm shift in electrical machine," ACEEE J. Elect. Power and Eng., vol. 3, no. 1, pp. 33-37, 2012.

[24] Trimble SketchUp Software for 2D/3D Modeling [Online]. Available: http://www.sketchup.com/.

[25] MATLAB and Simulink Software for Technical Computing [Online]. Available: http://www.mathworks.com/.

[26] J. F. Gieras, R. J. Wang and M. J. Kamper, Axial Flux Permanent Magnet Brushless Machines, 2nd ed., New York, Springer, 2008.

[27] Finite Element Method Magnetics Software for Two-Dimensional Planar Electromagnetic Modeling [Online]. Available: http://www.femm.info/wiki/HomePage /.

[28] M. R. Patel, Wind and Solar Power Systems, Florida, CRC Press, 1999.

[29] S. M. Muyeen, J. Tamura and T . Murata, Stability Augmentation of a Grid-connected Wind Farm, New York, Springer, 2009.

[30] A. G. González Rodriguez, A. González Rodriguez and M. BurgosPayán, “Estimating wind turbines mechanical constants,” in Int. Conf. Renewable Energies and Power Quality, Seville, Spain, 2007, no. 361, pp. 1-8.

[31] P. C. Krause, O. Wasynczuk and S. D. Sudhoff, Analysis of Electric Machinery and Drive Systems, 3rd ed., New Jercey, IEEE Press Series on Power Engineering, John Wiley & Sons, 2013.

[32] R. J. Wang, M. J. Kamper, V. D. Westhuizen and J. F. Gieras, “Optimal design of coreless stator axial flux permanent -magnet generator,” IEEE Trans. Magn., vol. 41, no. 1, pp. 55-64, 2005.

57