Optimal Design of Permanent Magnet Synchronous Generator for ...

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Optimal Design of Permanent Magnet Synchronous Generator for Wind Energy Conversion Considering Annual Energy Input and Magnet Volume Jawad Faiz, Bashir Mahdi Ebrahimi and M. Rajabi-Sebdani and A, Khan Abstract— In this paper a multi-objective criterion function is introduced to maximize annual energy input (AEI) and minimize permanent magnet (PM) volumes in a permanent magnet synchronous generator (PMSG). First, a PMSG is designed and modeled analytically to achieve above mentioned targets. After that, effects of various generator parameters on the two abovementioned objective functions are analyzed using this model. The PMSG parameters and dimensions are then optimized using a genetic algorithm incorporated with an appropriate objective function. The results demonstrate an considerable enhancement in PMSG performance. Thus, Finite element method (FEM) is utilized to prove the analytical results. Comparison between simulation and experimental results presents a good agreement between estimated and practical results. Index Terms— Permanent magnet synchronous wind generator, optimization, genetic algorithm, annual energy, finite element.

I. INTRODUCTION

P

ERMANENT magnet wind generators are used in variable speed, direct-driven wind energy conversion systems (WECS), whilst induction generators are used in constant, semi-constant speed and geared systems [1]. If speed of generator varies with wind speed, the wind generator may be used at the peak power and received the maximum power from the wind [2]. Eliminating the gear-box between the generator shaft and wind turbine such varying speed generator is possible [3, 4]. In addition, removing the gear-box has a number of benefits including: reduction of the system complexity, lack of lubrication, eliminating the extra losses and acoustic noise [4]. Although induction generators themselves are powerful and non-expensive, they require bulky and expensive capacitance [5] for generator-mode operation and reasonable performance is provided by excitation control. Over-voltage and over-current are their operational difficulties which must be solved in the speed Manuscript received December 31, 2008. Jawad Faiz in with University College of Nabeei-Akram, Tabriz, Iran, Bashir Mahdi Ebrahimi and M. Rajabi-Sebdani are with the Center of Excellence on Applied Electromagnetics Systems, Department of Electrical and Computer Engineering, University of Tehran, Tehran 1439957131, Iran (phone: +98 21 88003330; fax: +98 21 88633029; e-mail: [email protected]). M. A. Khan is with Department of Electrical Engineering, University of Cape Town, Cape Town 7701, South Africa.

carrying case. Permanent magnets are easily available and their costs are gradually decreasing, use of the PM generators, particularly over these speeds, are getting popular. Advantages of the PM generators include simple design of rotor, lack of slip rings and generator excitation, lower temperature rise and consequently improvement of the efficiency [6].PM generators are classified into four groups: radial flux, axial flux, and cross-field and tooth pole. It has been proved that most wind PM generators are radial flux and axial flux types. The inner rotor, radial flux PM generators are more popular due to their low cost and easy constructer. In [4], Three 500 kW wind generators consists of; 1) a 4-pole, , fixed speed induction generators with gear-box, 2) a fixed speed synchronous generator with gear-box, frequency converter, 3) a variable speed PM generator with no gear-box with frequency converter have been studied and it has been shown that gearless PM generator has higher efficiency over all speeds and ;loads because of lower core losses, rotational losses and gear losses over low speeds. In modular design of radial flux PM generator, it consists of several modules and any module contains a standard Ferret PM block which magnetized in tangential direction. Stator consists of several modules and each module has an E-shaped core and each coil generates a single-phase alternating output. The outputs of the modules are separately rectified and they are combined in a general linkage dc with each other. If the rotor eddy current losses become larger than the permissible value, the rotor modules must be redesigned based on the concentrated flux within the sheets. In [7], the modular generator has been compared with the continuous core generator in [6] and it has been shown that the manufacturing of these types of generators are easier, reactances are lower and influence of the air gap flux harmonics components are less. However, it must be noted that the extra losses of the design has not been yet determined and controlled. In [8], two gearless inner PM (IPM) and surface-mounted PM (SPM) wind generators have been designed and the electromagnetic behavior as well as PM shape has been optimized using FEM. The result indicates that the torque ripple of SPM generator is lower than that of the IPM generator. In [9], the position of the rotor and stator in an external rotor generator has been exchanged and designed [9]. It has been shown that the generator can operate well over a wide range of the speed. In [10], radial flux SPM generators with two types of the stator

2 windings (distributed and concentrated) have been studied and shown that the consumption of the active materials, torque ripples and pull-out torque in the generator with the distributed winding is lower than that of the concentrated winding generator. In [11], a twin-rotor radial flux PM generators with loop-winding have been designed in which the torque density and efficiency have been improved, In addition, a Ferrit PM has been utilized in order to reduce the cost and cogging torque and improve the efficiency. In all generators designed in [2-11], the PM has been used continuously; if PM is discretized over each pole, the structure will be simpler and cost reduce. The reason is that a smaller PM does not need a curvature. Meanwhile, the discritizing PM and choosing a proper clearance between the PMs on each pole decreases the harmonics effect. In this paper a inner-rotor, radial-flux PM generator which has the simplest structure and more general has been taken. The stator is identical to that of the induction machine. The PM has been placed on each pole of rotor surface in disctritized manner in order to reduce the cost. Optimization of the generator is carried based of an analytical method and necessary changes in the generator; then it is compared with the optimal design reported in [12]. II. ANALYTICAL DESIGN Analytical design of the wind turbine is considered in this section. In particular, the turbine blade sizing and the maximum power coefficient of the wind turbine are discussed. A. Turbine Blade Sizing and Shaft Speed

Fig.1. Variation of shaft power with turbine speed

T sh a ft =

Ps h a f t

=

ωr

1 ρ a ir π R 3 U 2

2

CT

(3)

where CT=Cp / λ is the torque coefficient of the turbine. The power captured by a wind turbine and turbine shaft speed for a PMSG has shown in Fig. 1. Generator out-put power (Pgen) can be expressed as follows: (4) P gen = η gen . Pshaft Combining (1) and (4), facilitates the sizing of a typical HAWT. In particular, R can be determined as a function of the rated output electrical power of the WECS and its operating wind speed as follows: R =

P gen 1 ρ 2

πU

air

3

C Pη

(5) gen

The rotor blade diameter and operating shaft speed of a small direct-drive WECS depend on its output electrical power and rated wind speed requirements. As an example, a high-power WECS operating in a high wind speed region could require smaller blades than a low-power WECS operating in a low wind speed region. It is therefore important that due consideration be given to the sizing of the turbine blades for any small wind generator design. The functional relationship between the parameters which determine the turbine blade sizing and shaft speed will be discussed further in this section. The power captured by a wind turbine (Pshaft) from the incident wind can be expressed as [2]: 1 (1) P = ρ π R2 U 3 C

Equations (1), (2) and (4) can be combined in a similar manner to determine the operating shaft speed as a function of the WECS output power and rated wind speeds. This can be expressed as:

where ρair is the density of air at the height of the turbine hub Cp is the dimensionless power co-efficient or aerodynamic efficiency of the turbine and R is the radius of the turbine blade. The power coefficient of the turbine is a function of the tip speed ratio (λ) at which the turbine is operating. This ratio is defined as the ratio of blade tip speed to wind speed, and can be expressed as [2]: ωr R (2) λ =

Equation (4) can be refaced as follows: d Pg e n d Pg e n d λ = . = 0 dωr dλ dωr It is necessary to note that

sh a ft

2

a ir

p

U

Equations 1 and 2 can be used to determine an expression for the torque applied to the turbine shaft, which can be expressed as:

ω

r

=

1 2

ρ

air

πλ 2 U 5 C P η

gen

P gen

(6)

B. Maximum power coefficient of the wind turbine Referring to Fig. 1 shows that power shaft maximization which can be expressed as follows [2]: dP gen dω r

(7)

= 0

d Pg e n dλ ≠ 0 → ≠ 0 dωr dλ

(8)

(9)

So, power shaft maximization can be found as follows: d Pg e n dωr

= 0 ↔

d Pg e n dλ

= 0 →

dC P (β , λ ) = 0 dλ

(10)

With defined Cp, the maximization Pgen and Pshaft will be defined.

3 III. PERMANENT MAGNET WIND GENERATOR DESIGN The PM wind generator design is considered in this section. In particular, the PM wind generator sizing, required number of generator poles, specific electric loading, annual energy input and PM material volume are discussed here. A. PM GENERATOR POWER The apparent power of a radial-flux machine at the air-gap can be written in terms of the main dimensions of the machine as follows [13]: 1 (11) S g = π 2 . K w 1 . D 2 .A .n s . S M L p k . S E L p k 2 where Kw1 is the fundamental winding factor, ns is the rotational speed in rev/sec, SMLpk and SELpk are the peak values of the specific magnetic and electric loadings of the machine. The output electrical power of a radial-flux generator can be related to its apparent air gap power by the following expression [14]: Ef (12) p gen = 3 V a I a cos ϕ = 3 I a cos ϕ

Fig. 2. Variation of excitation voltage with rotor speed

ε

where ε= Ef/Va and Ef is excitation voltage as [14]:

E f = 2 π f N ph kω1 ϕ p

(13)

where φp is the flux per pole due to the fundamental space harmonic component of the excitation flux density distribution, f is the frequency and Nph is the number of turns per phase. Resulting rms value of the fundamental excitation voltage calculated for this machine at various speeds has been shown in Fig. 2. According to Fig. 2, increases slope of excitation voltage amplitude in presented optimization generator more than 2.5 times of initial generator. Indeed, presented generator can make out-put voltage larger than the initial generator in low speed of wind. Variation of terminal voltage versus current has been illustrated in Fig. 3 over different loads and power factors at the rated speed. The calculated core loss, rotational loss and total losses have been shown in Fig. 4. B. PM Wind Generator Size The machine under investigation has radially magnetised NdFeB PMs mounted on the surface of a solid mild-steel rotor core. The stator core consists of silicon sheet steel laminations with semi-closed rectangular slots. The product D2ℓ,which is proportional to the rotor volume of a radial-flux machine, determines its output torque capability. This product can be determined by combining (10) and (11), and can be expressed as [15]:

ε Pgen

(14) 0.5 π K w1 .n s .SM L pk .SEL pk .C osϕ where the D2ℓ is determined from (14), the relative apportionment of D and ℓ in a conventional radial-flux machine design is purely based upon practical requirements of the machine application [15]. This is facilitated by the choice of a suitable aspect ratio coefficient, defined as KL= ℓ/D, for each application. Typical values of KL reported in the literature vary widely from 0.14 to 0.5 for direct-drive PM wind generator applications [2],[16],[17], [18]. In choosing the air gap diameter in a radial-flux PM wind generator design, due

D 2 .A =

2

Fig. 3. Terminal voltage characteristic of an PMSG at various load power factors and rated speed

Fig. 4. Variation of rotational and core losses with rotor speed

consideration should be given to the number of poles required and hence the resulting pole pitch of a design. The diameter should however be restricted in order to limit the proportion of inactive copper in the overhang [13]. C. Number of Generator Poles The operating frequency range for small PM wind generators is reported as typically:30-80 Hz [12] and 10-70 Hz [9]. Thus, the nominal frequency of the generator at rated wind speed is chosen to be within the range 45-65 Hz. The required number of generator poles for various WECS output powers and rated wind speeds are: TABLE I.

4 DESIGN CONSTRAINT Parameter Minimum Value Terminal Voltage (V) 180 Axial Length (m) 0.04 Pole arc to Pole pitch ratio 0.556 Remnant of flux density (T) 0.8 Area of conductor (mm) 1.257 SEL A/m 10000 Efficiency (%) 80 Power Factor 0.7 Wind speed (m/s) 7

p = 2π f

Maximum Value 240 0.08 0.9 1.4 4.398 40000 100 0.9 12

P gen

(15) ρ air πλ 2 U 5 C P η gen Poles number for generators operating at a nominal frequency of 50Hz, as a function of Pgen, at various rated wind speeds are illustrated in Fig.5. The figure is applicable to both radial and axial-flux PM wind generators. 1 2

D. Specific Electric Loading The specific electric loading of a machine is the circumferential current density of the stator. It is limited by the slot-fill factor, slot height and current density of stator conductors [15]. The range of specific electric loadings (SEL) for small PM machines is typically: 10,000 --- 40,000A/m [13]. 6 N ph I ph (16) SEL = πD The slot-fill factor (Ksf) is defined as the ratio of copper to slot area and is usually in the range: 0.3-0.5 for small low-voltage machines [1],[15]. This range ensures that the stator cores can be easily wound. May be tolerable in small PM wind generator designs provided that the insulation class of the windings is at least F, and that adequate cooling is provided [14]. Since the wind cool up the wind generator, the current density must be lower than 3 A/mm2 to prevent the temperature rise of the windings over the permissible value [19]. E. Annual Energy Input The wind data for any region is modeled by Vibal or Railey distribution. For a Eailey distribution over different speeds the following equation can be written [2]::

π Ui

π U − ( i )2 4 U

(17) 2U2 Where U1 is the wind speed at any time and U is the mean wind speed at the proposed region. The total hours with speed U1 over one year with simplification of probability of its occurrence can be given as follows: (18) H (U i ) = 365 * 24 * f (U i )ΔU

f (U i ) =

e

The annual output energy of wind energy is [2]: n

AEO = ∑ P(U i ) * H (U i )

(19)

i =1

Where P(U1) is the output of the wind energy converter at speed U1.

Fig. 5. Number poles for generators operating at a nominal frequency of 50Hz, as a function of Pgen, at various rated wind speeds

F. PM material Volume The PM material volumes (Vpm) can further be expressed as:

V pm = α .π .l ( D − 2l g − lm )

(20)

where α is the PM arc length and pole pitch ratio, lg is the air gap length and lm is the PM radial length. IV. OPTIMIZATION ALGORITHM Some of the typical PMSG and dimensions are selected as design variables where values are determined through an optimization procedure. In this paper, design variables are axial length, remanent flux density of the PMs, specific electric loading, efficiency, power factor, terminal voltage and wind speed. To have a more realistic design, some constraints are applied to design variables listed in Table I. The pole pairs, rated frequency, number of blades, main fixed specifications in the design procedure are (250 rpm), 50 Hz and 3 respectively. To obtain an optimal design considering, annual energy input (AEI) and PM volume, the two objective functions are defined as follows: AEI ( x1 , x2 ,..., xn ) m (21) J z ( x1 , x2 ,..., xn ) = VPM ( x1 , x2 ,..., xn ) n where x1, x2, … xn are design variables. As seen in (21) the importance of the annual energy input and PM material volume are adjusted by power coefficients. Maximization for Jz fulfils simultaneously two objectives of the optimization. Such an objective function provides a higher degree of freedom is selecting appropriate design variables. Genetic algorithm provides a random search technique to find a global optimal solution in a complex multidimensional search space. The algorithm consists of three basic operators i.e., selection, crossover and mutation. In this paper, roulette wheel method is used for selection and each step elite individual sent directly to the next population. Table II shows the genetic algorithm parameters used in this paper. A threephase PMSG for handling materials application is chosen as the basis of design optimization. The minimum value of the terminal voltage, annual energy input, PM material volume and power factor in the algorithm is chosen close to their TABLE II GENETIC ALGORITHM PARAMETERS

5 Parameter

Value

Probability of crossover Probability of mutation Population size Number of Generations

0.7 0.05-0.15 45-55 600

initial values of the non-optimized generator. In a practical design the efficiency must be paid attention, because optimization may lead to undesirable reduction of the efficiency. However the efficiency of any design must not be lower than 80%. The results of this optimization have been summarized in Table III. A. Maximization of AEI In this case we aim the maximum annual energy input (AEI) for which the values of m and n were set to 1 and 0, respectively. Third column in Table III summaries the parameters obtained by the optimization for machine. Comparing the results obtained from the optimization with those of original generator, shown in the second column of Table III, it can be seen that the annual energy input increases more than 64%. On the other hand the efficiency of machine and magnet volume has increased as much as 5.6% and 26% respectively. Due to the fact that cost is a fundamental design parameter and magnet volume, as an expensive element, needs to be considered in designing the optimization discussed here seems not to be economical. So in the next section the optimization will focus on minimization of the magnet volume. B. Minimization of PM Material Volume At second optimization we set m to 0 while setting n to 1. So in this optimization we will only minimize PM volume. Machine dimensions and parameters are summarized in the forth column of Table III. The values reveal that PM material volume has decreased compared with the original generator. This is where the excitation voltage has increased three times along with the power factor increase of 27.2%. It is noteworthy that in this optimization the AEI has increased as much as 28.76%. C. Objective Optimization Considering sections A and B mentioned above it is obvious that Multi-Objective optimization is necessary to reach the AEI and minimum PM material volume. To do this we set the values of m and n to 1 in cost function. Although values of these parameters depend on the designer and on the expected performance of the machine but the same emphasis is applied here on these two parameters. Obtained values from optimization are shown in the fifth column of Table III, simplifying the comparison of this optimization with others. The comparison of the optimization results with original generator reveals that annual energy input has increased more than 34% times. On the other hand, considering table III it is seen that the efficiency has increased 4.17% where PM volume decreased 18.8, excitation voltage increased 3.38 times and output power increased about 9%.

a

b Fig. 6. Variation of excitation voltage with time, (a) original PMSG and (b) propose optimal design

V. FINITE ELEMENT ANALYSIS The first step in prediction and analysis of the PMSG is the precise modeling of the motor. The motor is modeled taking into account the non-linearity of the ferromagnetic materials and the physical conditions of the motor components. The local total current density (J) is: (22)

J = J 0 − jω Α

where J0=σE0 is the current density due to the supply voltage and A is the magnetic potential vector. The total current in a conductor having cross-section Ωb is: (23) J .d s = J − jωσ Α dξ

∫(

∫

Ωb

0

Ωb

For every circuit: ν s = Rext i + Lext di dt + Es where

)

(25)

ν s is the impressed voltage, i is the phase current, Rext

is the stator phase resistance and Lext is the end winding inductance. and: N

Ε s = A m ∑ ± Εi

(26)

i =1

where lm is the length of the FE region, Zext is the external circuit impedance and N is the number of turns. By the following definition: V Ζ (27) v s = s , Ζ e = ext Am Am The following can be obtained:

6 TABLE III SPECIFICATIONS OF INTIAL AND OPTIMAL DESIGNED GENERATOR Proposed Optimal Design Original PMSG Parameters Number of turn per phase Cross sectional area of conductors (mm2) Specific electrical loading (A/mm2) Axial length (m) Pole arc to pole pitch ratio Remanent flux density of PM Wind speed (m/s) Power factor Ef(V) Efficiency Output power Annual energy capture (Wh) Volume of PM (m3)

m=1 and n=0

m=0 and n=1

m=1 and n=1

1152 936 816 2.5665 2.4584 3.6106 22191 23897 21251 0.0797 0.0499 0.0581 0.9574 0.6 0.8411 1.2838 1.3873 1.1512 9.5386 8.540 8.6304 0.8984 0.8904 0.8932 556.0489 239.9748 247.0602 93.45 88.2 92.03 2989 1625 1785 2.4261e+007 1.9000e+007 1.9911e+07 23.175×10-5 9.0853×10-5 14.824×10-5 N [2] dissertation, Dept. Elec. and Comp. Eng., Clarkson Univ.,Potsdam, NY, (28) vs = ± Ε i + Ζ e i Nov. 2006. i =1 [3] D. S. Zinger, E. Muljadi, "Annualized Wind Energy Improvement Using Variable Speeds," IEEE Trans. Industry Applications, vol. 33, No. 6, The matrix form of (28) is as follow: Nov./Dec. 1997, pp. 1444-1447. T (29) [Vs ] = [D] [Ε] + [Ζext ] [Ib ] [4] A. Grauers, "Efficiency of three wind energy generator systems," IEEE By combining the above equations, the following general Trans.Energy Conv., Vol. 11, No…., pp. 650-657, Sep. 1996. [5] A. Grauers, ‘‘Design of direct-driven permanent-magnet generators for system is obtained: wind turbines,’’ PhD Thesis, Chalmers University of Technology, ⎡ Α ⎤ −1 Goteberg, Sweden, Oct. 1996. 0] ⎤ ⎡ 0 ⎤ [ ⎢ ⎥ ⎡[S ] + jωσ xy [Τ] − jωσ z [C ] (30) [6] T.F.Chan,L.L. Lai,’’ An Axial-Flux Permanent-Magnet Synchronous ⎢ 0 ⎥ ⎥ ⎢ ⎥ = ⎢ − jωσ [C ]T jωσ z [Ωb ] − jω [D ] ⎥ ⎢ z ⎥ ⎢ Εs ⎥ ⎢ Generator for a Direct-Coupled Wind-Turbine System’’ IEEE Trans. on T ⎢ jω ⎥ ⎢⎣ [0] − jω [D] − jω [Ζ ext ]⎥⎦ ⎢⎣− vs ⎥⎦ Energy Conversion, Vol. 22, No.1, pp.86-94, March 2007. ⎢Ι ⎥ [7] E.Spooner, A.C. Williamson, "Direct coupled, permanent-magnet b ⎢ ⎥ generators for wind turbine applications," IEE Proc. B, Electr. Power ⎣⎢ jω ⎦⎥ Appl., Vol. 143, pp.1-8, Jan. 1996. where [Ib] is the circuit vector (number of circuits multiplied [8] E. Spooner, A.C. Williamson, G. Catto, "Modular design of permanent by 1), [Es] is the bar voltage vector (number of bars multiplied magnet generators for wind turbines," IEE Proc. B, Electr. Power Appl., by 1), [D] is the connection matrix of the bar (number of Vol.143, pp. 388-395, Sep. 1996. circuits multiplied by the number of bars), [Ωb] is the diagonal [9] S.A .Papathanassiou, A.G.Kladas, and M.P.Papadopoulos, "DirectCoupled Permanent Magnet Wind Turbine Design Considerations," matrix of the cross-section of the bar (number of the bars Proceedings of the European Wind Energy Conference(EWEC'99), Nice, multiplied by 1), [Zext] is the diagonal external impedance France, 1999 pp.1-4. matrix and vs is the circuit voltage vector (number of circuits [10] J. Chen, C.V. Nayar, and L. Xu, "Design and finite-element analysis of multiplied by 1). By solving (30), the magnetic potential an outerrotor permanent-magnet generator for directly coupled wind turbines," IEEE Trans. on Magnetics, Vol. 36, No…, pp. 3802-3809, Sep distribution within the machine, stator phase current and 2000. terminal voltage is obtained. Fig. 6 depicts the optimized excitation voltage compared with the voltage of the original [11] P. Lampola, ‘‘Directly driven, low speed permanent-magnet generators for wind power applications,’’ PhD Thesis, Helsinki University of generator. Technology,Helsinki, Norway, May 2000. [12] Q. Ronghai and A. Thomas, "Dual-rotor radial-flux toroidally wound permanent magnet machines",IEEE Trans. on Industrial Applications, VI. CONCLUSION Vol. 39, No. 6, November/December 2003, pp.1665-1673. A multi-objective optimization method was applied to a [13] M. A. Khan, P. Pillay, and K. D. Visser, "On Adapting a Small PM Wind PMSG to optimize the AEI and PM material volume Generator for a Multiblade, High Solidity Wind Turbine", IEEE Trans. Energy Conversion, Vol. 20, No. 3, pp.1619-1626, Sep. 2005. simultaneously. The analytical method was used this [14] M. G. Say, The Performance and Design of Alternating Current calculation. Comparison of the optimization results with Machines,3rd ed., London: Pitman and Sons, 1965. original generator reveals that annual energy input has [15] J. F. Gieras, M. Wing, Permanent Magnet Motor Technology: Design increased more than 34%. It is seen in Table III that the and Applications, 1st Ed., New York: Marcel Dekker, 1997. efficiency has increased 4.17% where PM volume decreased [16] T. J. E. Miller, Brushless Permanent-Magnet and Reluctance Motor Drives, New York: Oxford University Press, 1989. 18.8%, excitation voltage increased 3.38 times and output power increased about 9%. The effect of different PMSG [17] G. R. Slemon, and X. Liu, "Core Losses in Permanent Magnet Motors," IEEE Trans. on Magnetics, Vol. 26, No…, pp. 1653-1655, Sep. 1990. parameters on the AEI and PM material volume were [18] A. M. De Broe’, S. Drouilhet, and V. Gevorgian, "A Peak Power investigated through appropriate TSFEM. PMSG parameters and Tracker for Small Wind Turbines in Battery Charging Applications," IEEE Trans. on Energy Conversion, Vol. 14, No. 4, pp. 1630-1635, Dec. dimensions were optimized using a genetic algorithm. 1999. [19] P. Pillay, R. Krishnan, "Modelling, Simulation, and Analysis of VII. REFERENCES Permanent-Magnet Motor Drives, Part I: The Permanent-Magnet Synchronous Motor Drive," IEEE Trans. Industry Applications, vol. 25, [1] M.A. Khan , " Contributions to Permanent Magnet Wind Generator Mar./Apr. 1989, pp. 265-273. Design Including the Application of Soft Magnetic Composites," Ph.D.

∑

372 4.398 25578 0.0665 0.905 1.17 10 0.7 72.89 87.86 1625 1.4756e+007 18.272×10-5