Optimal Design of Six-phase Permanent Magnet Synchronous ... · PDF fileOptimal Design of...

International Journal of Scientific Research in Knowledge, 2(8), pp. 381-394, 2014

Available online at http://www.ijsrpub.com/ijsrk

ISSN: 2322-4541; ©2014 IJSRPUB

http://dx.doi.org/10.12983/ijsrk-2014-p0381-0394

381

Full Length Research Paper

Optimal Design of Six-phase Permanent Magnet Synchronous Generator for direct-

drive Small-Scale Wind Turbines

Mohammad Ebrahim Moazzen*, Sayyed Asghar Gholamian

Babol University of Technology, Babol, Iran

*Corresponding Author: Email: [email protected], [email protected]

Received 21 May 2014; Accepted 29 July 2014

Abstract. Permanent Magnet (PM) generators are widely employed in directly coupled wind turbines. Therefore, optimal

design of these generators is quite necessary to improve their overall performance. In this paper, single/multi-objective design

optimization of six-phase permanent magnet synchronous generator (PMSG) for directly coupled wind turbines is carried out.

The studied PM generator in this paper is the radial-flux surface mounted PM generator. The aim of optimal design is to reduce

the cost of PMSG manufacturing and generator losses. For this purpose, the main equations of PM generator design are

extracted. Therefore, the generator design steps are developed and then imperialist competitive algorithm is used to optimize

the design variables of the generator. To find the best design for this generator, the cost and losses, separately, are optimized

and are then optimized simultaneously. Finally, the optimum results are presented. Comparison between optimum results

shows that simultaneous optimization of the cost and losses leads to suitable design for PM wind generator.

Keywords: Permanent Magnet Generator, Wind power, Optimal Design, Imperialist Competitive Algorithm

1. INTRODUCTION

Today, renewable energy is rapidly replacing with the

other traditional sources of electricity generation like

coal, gas and nuclear power. The contribution of wind

energy in electricity generation, as one of the most

important types of renewable energy sources, has

grown swiftly over the past decade. At the end of the

year 2013, global installed wind power capacity is

around 318 GW (Global Wind Report, 2013). In the

last two decades, In order to maximize the energy

capture, minimize costs and improve power quality,

various wind turbine concepts have been developed

(Gundogdu and Komurgoz, 2012). According to the

construction of drive trains, there are two types of

wind turbine systems, namely, the geared drives and

the direct-drive systems (Li et al., 2009).

The some advantages of direct-drive system

compared to the geared drive are as: high overall

efficiency, high reliability and low maintenance due to

omitting the gearbox (Li et al., 2009; Grauers, 1996).

Different types of generators can be used in direct-

drive wind turbine. The generators used in the market

can be divided into electrically excited generators and

permanent magnet generators (Gundogdu and

Komurgoz, 2012). High power density, high

reliability and high efficiency are the advantages of

permanent magnet generators compared to the

electrically excited generators (Widyan, 2006). Over

the last few decades, several studies have concentrated

their research on the PM wind generator, for example:

In (Grauers, 1996), a PM synchronous generator is

compared to an induction generator, which it is shown

that the efficiency of PMSG can be more than

induction generator. In (Chen et al., 2000), outer-rotor

permanent-magnet generator for directly coupled

wind turbines has been studied. It is shown that a

generator with a simple construction can operate with

good and reliable performance over a wide range of

wind speeds. An optimal design procedure for

permanent-magnet (PM) wind generator based on

maximizing the energy yield from the generator is

introduced in (Khan and Pillay, 2005).

In (Li and Chen, 2009), forty-five direct-drive PM

wind power generator systems with the different rated

power level and different rated rotational speed have

been optimally designed for the minimum generator

system cost. Finally, the optimum results have been

compared to each other. In (Duan et al., 2010),

optimal design and finite element analysis of 2 MW

direct drive permanent magnet wind generator has

been proposed. The results indicate that to improve

the EMF and reduce the flux leakage, the best pole-

slot number and the optimal structure of pole shoe can

Moazzen and Gholamian

Optimal Design of Six-phase Permanent Magnet Synchronous Generator for direct-drive Small-Scale Wind Turbines

382

be obtained by the comparison of different models. In

(Eriksson and Bernhoff, 2010), loss evaluation and

optimal design for direct-drive wind power generator

have been proposed. Also, it is expressed that an

optimized generator for a minimum of losses will

have a high overload capability. In (Abbasian and

Hassanpour, 2011), optimal design for minimizing the

payback period of the initial investment on direct-

drive PM wind generator systems, based on genetic

algorithm method, has been proposed. In (Pinilla and

Martinez, 2012), the optimum design of permanent-

magnet direct-drive generator, considering the cost

uncertainty in raw materials, is developed with genetic

algorithm. Design and study of the behavior for a

direct drive PMSG have been proposed in (Mihai et

al., 2012) and the effect of the positioning of the

permanent magnets on the rotor surface, concerning

spatial harmonics of the air gap flux density curve is

investigated. It is shown that the choice of an

increased air gap leads to improved voltage

waveform. Potgieter and Kamper (Potgieter and

Kamper, 2012) have presented a cost-effective

technique to reduce the cogging torque and improve

the voltage quality in PM wind generators. In (Tapia

et al., 2013), a simple analytic optimization algorithm

based on a well-known mathematical approach-

Lagrange multiplier- is used to maximize the apparent

air-gap power transferred under tangential stress

constraint for PM generator. A direct-drive wind

power generator has to operate at very low speeds.

Therefore, in order to produce electricity in a

normal frequency ranges (10-70 Hz or 30-80 Hz),

generator needs to have a large number of poles (Chen

et al., 2000; Khan and Pillay, 2005). In order to use

the direct-drive generator in variable speed operation,

the direct-drive PMSG connected to the grid via back-

to-back power electronic converter, as illustrated in

Figure 1. Different topologies of PM machines are

possible to be used for direct-drive wind turbines but

the radial flux, surface mounted permanent magnet

generator, due to simple structure and reliability, can

be a good choice for this application (Li and Chen,

2009). This machine is shown in Figure 2. This paper

focuses on the optimal design of inner rotor direct

drive PMSG which uses surface magnetic poles and

radial direction magnetic circuit. To this end, the

equations needed for radial flux permanent magnet

synchronous generator design are extracted and then

the imperialist competitive algorithm is used to

optimal design which leads to minimize the cost of

PMSG Manufacturing and generator losses. The

selected permanent magnet material in this paper is

the NdFeB, which its remanent flux density is 1.23

(T) (Mohammadi and Mirsalim, 2014).

In this paper, the main equations needed for radial

flux permanent magnet (RFPM) synchronous

generator design are presented in Section 2. Generator

losses are introduced in Section 3. Wind turbine

modeling and calculating shaft speed are presented in

Section 4. In Section 5, cost estimation for PMSG

manufacturing is presented. The design procedure is

expressed in Section 6. In Section 7, Imperialist

competitive algorithm is introduced. Generator

parameters and design variables are given in Section

8. In Section 9, optimal design is carried out. Finally,

conclusions are given in Section 10.

2. MAIN EQUATIONS OF RFPM

In this section, the determination of the main

dimensions of a RFPM machines is investigated. In

this paper, parallel-sided teeth are rectangular and

stator slots are trapezoidal, as illustrated in Figure 2.

2.1. Main Dimensions

Geometrical parameters are calculated based on the

magnetic equivalent circuit of the machine (Bianchi et

al., 2006). In order to establish an analytical

relationship between the electromagnetic parameters

and geometric dimensions of the machine, the air-gap

apparent power is expressed as a function of the

induced voltage and current on the armature (stator)

winding as follows (Tapia et al., 2013; Gieras, 2010):

g

Where m is the generator number of phases. is

the no-load rms voltage induced in one phase of the

stator winding (EMF). is the stator rms current.

The air gap apparent power of the generator as a

function of main dimensions is given by (Gieras,

2010):

Where is the fundamental winding factor.

is the is the rotational speed in rev/sec. D is the air-

gap diameter (stator inner diameter). L is the armature

stack length. is the peak value of the first

harmonic of the air gap magnetic flux density, which

as follows (Li and Chen, 2009; Gieras, 2010):

Where and are the peak value of the air

gap magnetic flux density and the pole-shoe arc to

pole-pitch ratio, respectively. In (Gieras, 2010), it has

been assumed that is equal to (

≈ ), but we have used in (2). The range of

values for is selected between 0.6 and 0.9

(Grauers, 1996). and are illustrated in

Figure 3. For the sizing procedure of NdFeB


383

Permanent Magnet synchronous machines can

initially be estimated as Bmg= (0.6 - 0.8) ×Br. Br is

the remanent flux density of the PM (Gieras, 2010). In

(3), is the peak value of the stator line current

density, which can be expressed as (Gieras, 2010):

√

Where is the number of turns per phase.

Finally, the main dimensions of the machine as a

function of the output power as follows (Gieras,

2010):

Where is the output power of the generator.

is the no-load EMF to phase voltage ratio. In this

paper, this parameter is used to regulate the terminal

voltage. is the output coefficients and can be

extracted from (2). We have determined the main

dimensions of the machine by selecting a suitable air-

gap diameter to armature stack length ratio (L/D). The

relative apportionment of air-gap diameter and

armature stack length in a RFPM design depends on

the machine application. The suitable range of values

for ratio L/D is typically 0.14 - 0.5 for direct-drive PM

wind generator applications (Khan and Pillay, 2005).



384

2.2. Stator and Rotor Sizing

The stator teeth, the back iron of the stator and rotor

provide the paths for flux. It is notice that to prevent

the saturation of these parts, adequate cross-sectional

area of these parts is provided. Hence, the back iron

thickness and the tooth width are expressed as a

function of the flux densities (Bianchi et al., 2006).

The back iron thickness (Stator or Rotor) can be

calculated as (Grauers, 1996; Li and Chen, 2009;

Bianchi et al., 2006):

Where is the pole-shoe arc. is the peak flux

density of the back iron. is the available length of

the stator core, which can be expressed as : = .

Where is the lamination stack factor of the stator

core. In this paper, = 0.97 is assumed (Grauers,

1996). The tooth width can be expressed as (Grauers,

1996; Bianchi et al., 2006):

Where and are the slot pitch and the peak

teeth flux density, respectively. Finally, the stator slot

area, neglecting the tooth tip and referring to Figure 2,

can be calculated as (Bianchi et al., 2006):

[

]

Where is the number of slots. and is the

outer diameter of stator and the tooth height,

respectively. The slot shape and its dimensions are

shown in Figure 4.

Table 4: Generator Parameters

2.3. Magnet Dimensions

The magnet thickness can be expressed as (Li and

Chen, 2009):

Where is the relative permeability of the PM

materials. is the effective air gap, which can be

calculated as (Li and Chen, 2009):

(

)

Where and is the Carter's coefficient and g is

the mechanical air-gap.

3. GENERATOR LOSSES

The generator losses are investigated in this section.

The losses considered in this paper are the stator iron

losses, the copper losses, ventilation and windage

losses and additional losses. The stator iron losses can

be divided into hysteresis losses and eddy current

losses. The rotor iron losses are neglected.

3.1. Core Losses

The stator iron losses in the separate parts, i.e., teeth

and back iron, estimated by determining the peak flux

densities in the teeth and back iron. Therefore, we can

use the equation (11) for calculate the stator core

losses, which can be expressed as (Li et al., 2009;

Grauers, 1996):

(

)

(

) (

)

Where is the core losses in the back iron or

teeth of the stator. f is the rated frequency of the

generator. and are the empirical factors for the

hysteresis and eddy current losses. is the weight

of the core in the back iron or teeth of the stator.

and , respectively, are the specific hysteresis and

eddy current losses (W/kg) in the core laminations at

frequency (50 Hz) and flux density

(1.5T). is the flux density in the back iron or tooth

of the stator. The iron used for the stator is

Surahammar CK-30 (Grauers, 1996). Values of ,

, , and are given in Table 1.


385

Table 5: Design variables and their variation boundaries

3.2. Copper Losses

The copper losses can be calculated as:

Where is the stator winding resistance per

phase, which can be expressed as:

Where is the copper resistivity (

at ) (Gieras, 2010). and are the Number

of turns per phase and the conductor cross section,

respectively. is the average length of the one turn

per phase, which can be calculated as:

Where is the end-winding length, which is

referring to Figure 5, can be approximated as (Bianchi

et al., 2006):

Where , is the slot pitch measured at the half

height of the stator tooth, which can be calculated by

(16). is the coil pitch (in number of slots). is the

increasing factor. This factor is considered due to the

end-winding overlapping. The range of values for

is 1.6 - 2 (Bianchi et al., 2006). = 1.8 is assumed

in this paper.

3.3. Windage and Ventilation Losses

The windage and ventilation losses can be calculated

as (Pyrhönen et al., 2008):

(

)

Where is an empirical factor, which depends on

the cooling system. = 10 is chosen (Pyrhönen et

al., 2008). , and are the rotor diameter, the

pole pitch and the rotational speed in rev/sec,

respectively.



386


387

3.4. Additional Losses

The additional losses are very difficult to calculate

and can be commonly determined as a fraction of the

output power as follows (Pyrhönen et al., 2008):

The range of values for is 0.0005 – 0.0015 for

Nonsalient-pole synchronous machine (Pyrhönen et

al., 2008). In this paper, =0.0015 is chosen.

4. WIND TURBINE MODEL AND SHAFT

SPEED

A wind turbine is a device that converts kinetic energy

from the wind into electric energy. The output power

from the wind turbine is ideally given by (Chen et al.,

2000; Jagau et al., 2012):

Where is the conversion efficiency with typical

values between 0.3 and 0.45 (Jagau et al., 2012).

is the air density (kg/m3). is the radius of the turbine

blade. u is the nominal wind speed. The rated speed of

the PMSG, largely, determines the overall size of the

generator. The nominal shaft speed of the PM wind

generator can be estimated as:

√

Where is the angular speed of the turbine shaft

as well as the PM generator shaft. is the generator

efficiency, which is assumed 0.9 (Li and Chen, 2009).



388

is The tip speed ratio, which can be expressed as

(Eriksson and Bernhoff, 2010; Jagau et al., 2012):

The range of values for is reported 5–7 and 6–8

(Li and Chen, 2009; Jagau et al., 2012). In this paper,

λ=6 is chosen. The wind speed is an important

parameter for calculating the nominal shaft speed.

According to the studies and researches previously

done by Iranian Renewable Energy Organization

(SUNA), the range of wind speed in the Nehbandan -

Zabol road of Iran, is 5-10.2 m/s (Iranian Renewable

Energy Organization, 2010). Therefore, our generator

has been designed to operate at the wind speed of 10

m/s. According to nominal wind speed, the shaft

speed is estimated 250 rpm. Therefore, the number of

poles to produce electricity in 50 Hz frequency and

nominal shaft speed is chosen 24.

5. COST ESTIMATION FOR PMSG

MANUFACTURING

In this section, the estimation of the cost of PMSG

manufacturing is described. This cost can be

expressed as (Gieras, 2010):

Where is the coefficient depending on the

number of manufactured generators per annum. In this

paper =1 is assumed. , , and are the

cost of winding, the cost of core, the cost of PMs and

the cost of shaft, respectively, which can be expressed

as (Gieras, 2010):

Where is the coefficient of the cost of

fabrication of coils (insulation, assembly,

impregnation, etc). is the coefficient taking into

account the cost of the rotor winding. is the

coefficient taking into account the cost of frame, end

bells and bearings. is the coefficient of utilization

of electrotechnical steel. is the stacking factor.

is the coefficient including the cost of stamping,

stacking and other operations. is the coefficient

accounting for the increase of the cost of PMs due to

complexity of their shape. is the coefficient

including the cost of magnetization of PMs. is

the total volume of the steel bar to the volume of the

shaft. is the coefficient taking into account the cost

of machining of the shaft. , , and are

the weight of the copper, the core, PMs and the shaft,

respectively. , and , respectively, are the

specific cost (U.S. dollars per kilogram) of the copper,

the core, PMs and the shaft steel. The different

coefficients of k and the different specific cost are

given in Table 2.

6. THE DESIGN PROCEDURE

The design procedure and flowchart is shown in

Figure 6. The main steps of generator design are

presented as:

(1) Initialize design values ( )

(2) Dedicate value to each design variables

(

)

(3) Calculate magnet thickness

(4) Computation of main dimensions (L and D) and

number of turns per phase ( )

(5) Calculate the geometrical dimensions of stator

(slot dimensions) and rotor

(6) Calculate the air-gap flux density and compare

to . If continue condition is satisfied continue, if

not go to 2.

(7) Calculate the cost of PMSG manufacturing and

generator losses

(8) Calculate the voltage induced ( ) and compare

to . If stop condition is satisfied stop, if not go to

2.


389

Fig. 6: Design flowchart of the radial flux, surface mounted PM generator

Start

Is there an empire

with no colonies

Eliminate this empire

Stop condition

satisfied

END

Assimilate colonies

Exchange the positions of that

imperialist and the colony

Is there a colony in an

empire which has lower cost

than that of the imperialist

Compute the total cost of all empires

Imperialistic Competition

Yes

Yes

Yes

No

No

No

Initialize the empires

Revolve some colonies

Unite Similar Empires

Fig. 7: Flowchart of imperialist competitive algorithm

7. IMPERIALIST OPTIMIZATION METHOD

In this paper, the optimization of permanent magnet

synchronous generator has been performed by

imperialist competitive algorithm (ICA). Optimization

of imperialist competitive algorithm has inspired from

a political-social process. Comparing to other

optimization methods, this method is much faster and

has high abilities. Figure 7 shows the proposed

algorithm stages. At first, we create a 1×Nvar array of

adjustable input parameters for generators which must

be optimized and then we called it a country. To start

the algorithm, Ncountry of the initial countries is created.

Nimp of the best members of this population (countries

with the lowest value of objective function) are

selected as imperialist. The rest of the Ncol countries,

make the colonial empires, each of them belongs to an

empire. The total power of each empire is modeled as

the total power of the imperialist countries, plus a

percentage of its colonies power average.



390

With the initial state of all the empires, colonial

competitive algorithm begins. Having the cost of all

imperialists, the normalized cost and as a result,

normalized relative power of each imperialist is

calculated and based on the above calculation, the

colonized countries are divided between these

imperialist. In the assimilation (absorption) policy of

the colonization process, the colony continues to

move in the direction approaching the imperialist,

with the amount of x unit and θ deviation. During the

move, some of the colonies might reach a better

position than the imperialist, which in this case the

colonies and imperialists change the roles and the

algorithm with the imperialist continues in a new

situations. The final stage of the imperialist

competition is the time when we have a single empire

with colonies very close to it. At this time, the

imperialist optimization method by reaching the

optimal peak of the objective function and considering

the stop criterion, is stopped (Atashpaz Gargari,

2008). The values of these parameters are adjusted to

achieve the desired goal in this paper by using

imperialist optimization method, in Table 3 is

obtained.

Fig. 8: The generator losses value at each iteration for the first 70 iterations

8. GENERATOR PARAMETERS AND DESIGN

VARIABLES

The optimal design in this paper is based on a 3500 w

direct-drive PM wind generator. The machine

parameters used in the optimal design are expressed in

Table 4. and are chosen 1 mm. =1.5 mm is

chosen. Design variables and their variation

boundaries are given in Table 5.


391

Fig. 9: The generator cost value at each iteration for the first 70 iterations

Fig. 10: The value of F3 at each iteration for the first 70 iterations

9. OPTIMIZATION OF PM WIND

GENERATOR DESIGN AND RESULTS

In this paper, the optimal design in order to

minimizing the cost of PMSG manufacturing and

generator losses has been done. To find the best

design for PM wind generator, Firstly, the generator

losses are optimized. Figure 8 depicts the generator

losses minimization for the first 70 iterations. The first

objective function as:

F1= + + + (28)



392

The second objective function is to optimize the cost

of PM wind generator, which can be expressed as:

F2= Ct (29)

Figure 9 plots the cost minimization for the first 70

iterations. The third objective function is to optimize

the cost of PM wind generator and generator losses,

simultaneously. This objective function can be

expressed as:

F3=

(30)

Where and β are minimum values of the PM

wind generator cost and generator losses, respectively.

Figure 10 plots the F3 minimization for the first 70

iterations. The dimensions of the optimal generator

and optimal values of design variables are listed in

Table 6.

Table 6: Optimal generator parameters

10. CONCLUSION

In this paper, by employing imperialist competitive

algorithm, single/multi-objective design optimizations

of 3.5 kw six-phase direct-drive permanent magnet

wind generator by choosing manufacturing cost and

generator losses and their combination as objective

function were performed. For this purpose, the main

equations of generator design are extracted and then

the cost and losses of generator are investigated. To

find the best design for this generator, firstly,

generator losses and then the cost of generator are

optimized. Finally, the cost and losses of generator

referring to (30), simultaneously, are optimized.

Referring to Table 6, the third objective function can

lead to the best design for the generator, because of

two reasons: First, compared to optimizing the losses,

the losses of generator only 14.51% is increased.

Second, compared to optimizing the cost, the cost of

generator only 5.64% is increased.


393

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Mohammad Ebrahim Moazzen was born in Mazandaran, Iran, in 1989. He is

currently working towards the M.Sc. degree in Babol University of Technology, Babol,

Iran.

Sayyed Asghar Gholamian was born in Mazandaran, Iran. He received the PhD degree in

electrical engineering from K.N. Toosi University of Technology, Tehran, Iran in 2008. He is

currently an assistant professor in the department of Electrical Engineering at the Babol

University of Technology, Babol, Iran. His research interests include design, simulation,

modeling and control of electrical machines.

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