International Journal of Smart Grid and Clean Energy

The optimal stator design of novel three-phase doubly salient

permanent magnet generator for improving the generator

output

V. Lounthavonga, W. Sriwannarat

a, C. Surawanitkun

b, R. Chatthaworn

a, A.

Siritaratiwata and P. Khunkitti

a,*

aDepartment of Electrical Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen 40002, Thailand bFaculty of Applied Science and Engineering, Khon Kaen University, Nong Khai Campus, Nong Khai 43000, Thailand

Abstract

As widely indicated in many recent studies that the Doubly Salient Permanent Magnet (DSPM) generator could

provide high electromotive force (EMF), this paper proposes an optimal structure design of DSPM generator for

improving the generator output. The finite element method was performed in the simulations and analysis. The

effects of stator structural parameters, including the thickness of permanent magnet (PM) and the inner stator depth

on the output characteristics of generator were demonstrated. The generator outputs including the magnetic flux-

linkage, magnetic flux distribution, EMF and voltage regulation were discussed. The results showed that the magnetic

flux-linkage and the EMF of proposed optimal structure could be significantly improved by an adjustment of the PM

thickness and stator depth. An optimal thickness of PM and inner stator depth regarding this particular generator was

chosen. The magnetic flux distribution analysis was also carried out to confirm the simulation results. It was found

that the optimal structure of DSPM can be achieved by increasing the PM thickness to be 150 % with reducing the

stator pole depth to be 80 % of the those conventional values. The flux-linkage and EMF produced by the proposed

optimal structure are 15.88 % and 6 % higher than that of conventional structure. Moreover, the optimal structure also

provides greater voltage regulation profile than conventional structure. Then, the optimal design of PM thickness and

inner stator depth regarding this particular generator model can be adapted any other PM machine design in order to

maximize the generator output.

Keywords: Permanent magnet machine, Doubly salient generator, Finite element methods, Electromagnetic force,

voltage regulation

1. Introduction

The permanent magnet (PM) machines have been extensively utilized in many applications, especially

in motor drive and electrical generator [1]. Due to an absence of field excitation and copper loss in

machine structure, several outstanding properties of these machines such as high torque density, high

output power, high energy conversion and machine efficiency have been widely indicated in many

literatures [1, 2]. The Neodymium Iron Boron (Nd-Fe-B) magnets has been widely used in PM machines

since it could bring out high reliability, torque density and power output properties of those machines [1-

3]. The PM machines can be classified into two main types, namely, the stator PM machines and the rotor

PM machines depending on the location of installed PM. The rotor PM machines have simple structure

and more robustness [1]. There many types of rotor PM machines depending on the location of PM e.g.

the surface mounted PM machine, the surface inset PM machine, interior radial PM machine and interior

* Manuscript received June 2, 2019; revised February 7, 2020.

Corresponding author. Tel.: +66-86-636-5678; E-mail address: piratkh@kku.ac.th. doi: 10.12720/sgce.9.2.314-322

circumferential. However, the main disadvantage of rotor PM machines is their high rotor weight because

the permanent magnets are totally mounted at the rotating part, then the rotor PM machines are suitable

for low operated speed applications [1, 2]. The stator PM machines normally contain both of the armature

winding and the permanent magnet at the stator, whereas the rotor part has no copper coil, PM and brush,

accordingly the rotor of these machines has lightweight and low inertia. The stator PM machines have

been widely researched in order to develop their performance, three machine structures are mostly

proposed in the literatures, i.e. the flux-reversal PM machine [4-6], the switch-flux PM machine [7-9],

and the doubly salient permanent magnet (DSPM) machine [10-12].

The flux-reversal PM machine comprises a pair of permanent magnets at different polarity mounted at

the surface of the stator [13-15]. This pair of magnet could increasingly improve the magnetic induction

through the structure. The flux-reversal PM machine is appropriate for brushless direct current operation

[16-18]. The switch-flux PM machine consists of two adjacent stator laminated segments separated by a

permanent magnet [7-9]. The main advantages of this machine are robust rotor and high torque density.

However, in the operation of switch-flux permanent machine, the armature winding wrapped around the

permanent magnet usually results in high thermal temperature, which could further cause the magnetic

degradation and core loss [18-20]. The DSPM machines, where the PMs are inserted in stator yoke, have

received much research interest because of their outstanding advantages such as higher efficiency, power

output density, better controllability and lower inertia and ripple torque than the other stator PM machines

[21, 22]. Therefore, it is appropriate for low-speed applications such as wind and hydro generators. A

development of these machines are widely researched using different technique e.g. designing new outer-

rotor structure for motor drives or wind power generation [23, 24], reducing eddy current effect [25]. A

novel three-phase doubly salient permanent magnet generator (DSPMG) was proposed by J. Zhang [26].

It was indicated that this particular structure could achieve high output power compares to other existing

models. However, we notice that the performance of this particular structure of DSPMG can be still

improved by modifying the generator components which are the thickness of PM and the depth of inner

stator pole, since these two factors are strongly related to the power output.

Then, this paper aims to improve the output of DSPMG by using the modified technique to design the

optimal configuration of two structural parameters including the PM thickness and stator pole depth. The

flux-linkage, electromotive force (EMF), magnetic flux circulation property and voltage regulation of

DSPMG were focused as the indicators representing the generator output. The simulations were based on

finite element method (FEM) using COMSOL software.

2. Machine Design

2.1. Structure topology selection

Fig. 1. Cross-section model of the 12/8 stator/rotor poles DSPMG with the indicating the adjusted parameters.

The cross-sectional perspective of conventional DSPMG model was initially designed by J. Zhang et

al., as illustrated in Fig. 1(a) [26]. The conventional model contains 12 inner stator poles and 8 outer rotor

poles, which can be written as 12/8 stator/rotor poles. The rotor and stator poles are salient pole. The

315V. Lounthavong et al.: The optimal stator design of novel three-phase doubly …

permanent magnets, brushes and windings are assembled at the inner stator. Four pieces of Nd-Fe-B

permanent magnet are mounted inside the stator yoke for providing the field-excitation. The stator poles

are wired by the winding coils, indicated as circle symbol. The outer rotor of the DSPMG has completely

no those mentioned compositions, therefore the rotor weight and inertia of this generator is very light.

The structural parameters of this DSPMG are detailed in Table 1. The influence of PM thickness and the

inner stator depth on the generator output will be carried out to determine their optimal scale.

Table 1. The structural parameters of 12/8 stator/rotor poles conventional DSPMG.

Parameters of conventional DSPMG Value Parameters of conventional DSPMG Value

Rotor pole number 8 Stator pole depth (mm) 18

Rotor outer diameter (mm) 150 Rotor pole depth (mm) 6

Rotor inner diameter (mm) 118 Number of turn/phase 344 Stack length (mm) 22 Rates speed (rpm) 3600

Air gap length (mm) 0.45 Permanent magnet number 4

Stator pole number 12 Permanent magnet thickness (mm) 6

Stator inner diameter (mm) 43 Number of phase 3

Stator pole arc (°) 13.5 Magnetic remanent (T) 1.08

Rotor pole arc (°) 15 The phase position difference (°) 15

2.2. Analysis of machine characteristics

The two dimensional finite element method (2D-FEM) is performed in the calculations using

COMSOL software. The focused parameters of generator output include the magnetic flux linkage, the

EMF and voltage regulation. It is noted that before adjusting the designed parameters, an accuracy of the

generator model was verified through a consistency of results given in this work and original solution.

Based on flux-linkage and inductances derived from the FEM, the EMF can be calculated by basic EMF

equation as following detail. The magnetic vector potential in Z-axis, Az, is firstly calculated by the

Ampere’s law of Maxwell’s equation, written as equation (1),

0

1z

z r e

AA B J

t

(1)

where Br is the remanent flux density of Nd-Fe-B permanent magnet which is 1.08 T.

Je is an externally generated current density which has a magnitude of 0 A.

μ0 is the vacuum permeability of air.

σ is the electrical conductivity of air.

The z-component of electric field, Ez, is calculated by substituting Az in Faraday's law as shown in

equation (2).

t

AE z

z

)( (2)

The flux linkage, , existed in the machine structure can be calculated by using equation (3),

dAAA

LN zlinkage (3)

where N is the number of turns of winding-coil.

L is the stack length in the z-axis.

A is the area of the winding cross-section.

316 International Journal of Smart Grid and Clean Energy, vol. 9 , no. 2, March 2020

The magnitude of EMF can be consequently calculated by using equation (4).

dAEA

LNEMF z (4)

It is noted that the flux-linkage and EMF of DSPMG structure were obtained at winding coil of stator

poles by using Two-Dimensional Finite Element Method (2D-FEM). The designed parameters of the

proposed DSPMG consist of the thickness of PM and the length of stator depth. Normally, the volume

PM is directly related the magnetic flux-linkage, accordingly there is the possibility that the flux-linkage

circulation existing in the generator can be improved by increasing the PM thickness. In the conventional

model, it is seen that inner stator area for installing the PM is still available, then thickness of PM can be

further adjusted. However, the limitation for the PM thickness adjustment is that the thickness of PM

must be less than the width of stator yoke for preventing the flux leakage in the structure. In addition, the

effects of inner stator pole depth on the generator output is investigated because it is directly related to the

available area for installing PM. In this work, the output characteristics of DSPMG, including the flux-

linkage, electromotive force (EMF), magnetic flux circulation property and voltage regulation, were

characterized with varying PM thicknesses from 3 to 21 mm and stator depths from 9 to 21 mm. The

maximum possible PM thickness of 21 is limited by the width of stator yoke whereas the range of inner

stator depth is defined by considering the sufficient area for armature winding.

3. Results and Discussion

3.1. Influences of PM thickness on the generator output

In this section, the influences of PM thickness on the flux-linkage and EMF of DSPMG were

examined. The range of PM thickness starting from 3 mm to 21 mm, which is 50 % to 250 % compared

to conventional scale, was focused. Figure 2 indicates the influence of PM thickness on the flux-linkage

of DSPMG. From Fig. 2(a), it is obviously seen that the flux-linkage is increased with increasing PM

thicknesses for all rotor angles. The maximum value of those flux-linkage behaviors, as summarized in

Fig. 2(b), shows that the flux-linkage is continually increased with increasing PM thicknesses. In general,

an increase in sizing of permanent magnet normally yields an enhancement of the magnetic flux produced

by the magnet itself. The produced magnetic flux-linkage obtained in this work depends on the quantity

of the magnetic flux circulated through the winding coil at inner stator pole. Then, the thicker PM could

supply higher magnetic flux to the winding than that of thinner magnet. Especially, we found that an

increase of PM thickness at smaller scale has more influence on the flux-linkage improvement than that at

higher PM thickness due to the magnetic saturation point. Figure 3 demonstrates the characteristic of

EMF produced by DSPMG with varying PM thicknesses. The EMF produced by conventional DSPMG

structure is consistent with that shown in ref [26]. As shown in Fig. 3(a), the overall EMF tends to be

increased with increasing the PM thickness. While taking a closer look at the maximum value of EMF,

Fig. 3(b) demonstrates that increasing PM thicknesses from 6 to 12 mm results in a rapid increase of EMF.

Then, the EMF reaches the maximum value of 255.72 V at a PM thickness of 15 mm. After that, it

decreases with increasing PM thicknesses above the saturation point of 15 mm. When increasing the PM

thickness over the saturation point, a refutation of flux linkage for producing the EMF is occurred as a

reason for EMF degradation. From the results, it is obviously indicated that the optimal PM thickness for

this particular DSPMG structure is 15 mm, which could produce higher EMF than the conventional

structure about 4.5 %. Then, this optimum thickness of PM will be selected to further examine the

generator output with varying a depth of inner stator.

317V. Lounthavong et al.: The optimal stator design of novel three-phase doubly …

(a) (b)

Fig. 2. (a) The flux-linkage at all rotor angles and (b) the maximum value of flux-linkage with varying PM

thicknesses.

(a) (b)

Fig. 3. (a) The EMF at all rotor angles and (b) the maximum value of EMF with varying PM thicknesses.

The flux distribution at no load condition of DSPMG with a PM thickness of 6 mm (conventional

structure) and 15 mm are shown in Figs. 4(a) and 4(b), respectively. It is indicated that the distribution of

magnetic flied through the generator structure is symmetric, which brings about a symmetrical flux-

linkage circulation at all range of PM thicknesses. In addition, there is the magnetic flux leakage existed

at outer rotor the air gap and inner air gap between PM poles and rotation shaft. Also, the magnetic field

circulated through the structure is increased when increasing the PM thickness which further improves the

derivative of magnetic flux for producing the EMF.

(a) (b)

Fig. 4. The magnetic flux distribution at no load condition of DSPM generator with a PM thickness of 6 mm

(conventional structure) and (b) 15 mm.

318 International Journal of Smart Grid and Clean Energy, vol. 9 , no. 2, March 2020

3.2. Influences of stator depth on the generator output

In this section, the dependence of magnetic flux-linkage and EMF of DSPMG on an adjustment of the

inner stator depth was examined using an optimal PM thickness of 15 mm. The stator pole depth of

DSPMG was adjusted by reducing from 18 mm to 9 mm, which is 100 % to 50 % of conventional value.

It is noted that the volume of permanent magnet is always filled up fully within the stator pole, then the

length of PM is also altered according an adjustment of stator pole depth. Figures 5 and 6 show the

magnetic flux-linkage and the EMF of the generator with various stator pole depths, respectively. As

indicated in Figs. 5(a) and 5(b), it is obviously found that the overall and the maximum magnitudes of the

flux-linkage is linearly enlarged with decreasing in stator pole depth until stator pole depth of 14.4 mm,

afterwards the flux-linkage decreased with reducing stator depth. In addition, Figs. 6(a) and 6(b) show

that EMF produced by the generator becomes higher when reducing the stator pole depth from 18 mm to

14.4 mm. After that, the EMF is reduced with decreasing stator pole depth below 14.4 mm. When

reducing the depth of inner-stator from 18 mm to 14.4 mm, it is found that the EMF produced by the

generator becomes higher. This is because the shorter stator pole depth yields larger space for installing

the permanent magnet. Then, a bigger magnet could produce higher magnetic flux circulated through the

generator structure, which further improves the magnitude of EMF. It is importantly noticed that reducing

the stator pole depth results in a smaller area for armature coil winding. Especially, a number of winding

turn typically has more influence on the EMF than varying the inner stator depth. In this investigation, it

is found that the winding area is enough for 344 winding turns only at stator pole depth above 14.4 mm,

otherwise the effect of decreasing winding turn has to be taken into account. As can be seen from Figs.

5(a) and 5(b), a decrement of the flux-linkage and the EMF at stator pole depth below 14.4 mm is due to a

reduction of winding turn. Therefore, an optimal stator pole depth regarding this generator structure

should be 14.4 mm which could raise up the EMF to 259.42 V or 6 % above the EMF produced by the

conventional structure. Essentially, the EMF produced optimal proposed structure is in high-range

compared to other structure of DSPM generator in same dimension [27-31].

(a) (b)

Fig. 5. (a) The flux-linkage at all rotor angles and (b) the maximum value of flux-linkage with varying inner stator

depth.

(a) (b)

Fig. 6. (a) The EMF at all rotor angles and (b) the maximum value of EMF with varying inner stator depth.

319V. Lounthavong et al.: The optimal stator design of novel three-phase doubly …

The flux distribution at no load condition of DSPMG with 15 mm PM thickness at stator pole depth of

18 and 14.4 mm are shown in Figs. 7(a) and 7(b), respectively. A symmetrical flux-linkage distribution

circulated through the structure is found. Similar to the Fig. 4, the magnetic flux leakage is still existed at

outer rotor the air gap and inner air gap between PM poles and rotation shaft. Also, the magnetic field

circulated through the structure is increased when reducing the stator pole depth which enhances the

derivative of magnetic flux for producing the EMF.

(a) (b)

Fig. 7. The magnetic flux distribution at no load condition of DSPMG with 15 mm PM thickness at stator pole depth

of (a) 18 mm and (b) 14.4 mm.

3.3. Voltage regulation analysis

The voltage regulation of proposed DSPMG was analyzed in load condition. The winding coil of 344

turns was assumed. The voltage regulation is indicated through the phase voltage magnitude at varying

load currents. Figure 8 demonstrates the voltage regulation of three DSPMG structures including the

conventional structure, the structure with optimal PM thickness and the structure with optimized both of

PM thickness and stator depth. The structure with optimized both of PM thickness and stator depth

indicates better voltage regulation and higher phase voltage than other structures, this structure also

indicates the widest load current range. Thus, the proposed DSPMG with PM thickness of 15 nm and

stator depth of 14.4 nm is selected as the suitable structure in this work.

Fig. 8. The voltage regulation of selected proposed DSPG structures.

320 International Journal of Smart Grid and Clean Energy, vol. 9 , no. 2, March 2020

4. Conclusion

In this paper, the influences of PM thickness and inner stator depth on the output characteristics of

DSPMG including flux-linkage and EMF were investigated in order to improve the output of this

particular generator model. The results indicated that an increase of PM thickness could improve the

magnetic flux-linkage existed in the generator, which further results in an enhancement of the EMF. The

optimal PM thickness regarding this particular generator was found to be 15 mm, which is 150 %

compared to the conventional thickness. The dependences of inner stator depth on the magnetic flux-

linkage and EMF were in addition examined based on the optimal PM thickness. From the results, an

increment of magnetic flux-linkage and EMF were observed by a variation of inner stator pole depth. The

suitable stator pole depth for improving the generator output was found to be 14.4 mm, which is 20 %

shorter than the conventional structure. The EMF produced by this suitable structure is 6 % higher than

that of conventional model. A symmetry of magnetic flux circulation through the generator structure was

also indicated. Moreover, the optimal proposed structure could provide better voltage regulation than the

conventional, which further implies the higher output power of this structure. Therefore, the results

indicate that output of this particular DSPM generator can be improved by using this proposed design

technique. The optimal design concept in this work can be utilized to maximize the generator output of

any other DSPM machines which are extensively researched nowadays.

Acknowledgements

This work was financially supported by Electricity Authority of Thailand (EGAT), Electricite du Laos

(EDL), EDL - Generation public company (EDL-GEN) and Thailand Research Fund (grant number

MRG-6180010).

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