Design of Permanent Magnet Synchronous Machines of a direct-driven generator with Emetor & FLUX2D

*Aasim Ullah, ** Mohammad Istiaque Reja, ***Fahad Mirza and *** Hafiz Ahmed *Dept. of Electric Power, Norwegian University of Science & Technology, (NTNU), Trondheim, Norway

**Dept. of Electrical and Electronics Engineering, Chittagong University of Science & Technology, (CUET), Bangladesh *** Dept. of Electrical and Electronics Engineering, Ahsanullah University of Science & Technology, (AUST), Bangladesh

Mail ID: aasim@kth.se

Abstract— The research for optimization tool of electrical machine has developed for decades. Permanent Magnet is a new addition in this arena. This paper describes the details design of a direct-driven generator designed with Emetor and Flux 2D. The initial analytical design is done with Emetor. Then the experimented result is verified with a FEM simulation software from Cedrat group named FLUX 2D. Emetor is an educational web-based design tool for permanent-magnet synchronous machines (PMSM). In this paper the result from Emetor will be verified and further development of this tool will be proposed. The development of such tool can save the valuable time of designer. And can play a significant rule in machine design technology.

Index Terms— Emetor, Flux2D, Flux weakening, Field weakening, Finite Elements, Machine Design, Magnet working point, PMSM.

I. INTRODUCTIION This part of the paper deals with the preliminary design of

PMSM for a wind generator application. The initial design is carried out using Matlab. The machine is further optimized using Emetor, a web-based analytical tool for the design of PMSM developed at the lab of “Electrical Machines and Power Electronics” at “Royal Institute of technology”.

Emetor [1] takes on inputs for topology, material, design and windings and makes thermal and electro-magnetic analysis of the given machine. The PMSM under-study has surface-mounted magnets with radial flux topology and distributed windings with q=1.

TABLE1. CONSTANT OR INITIAL GIVEN PARAMETERS OF MACHINE

General Performance Mechanics Others Motor type:

radial-flux PM Motor

Topology: inner

rotor

Number of phases: 3

Shaft power: 1.5 MW at 100%

cycle

Nominal speed: 30 rpm

Nominal

voltage: 3 kV

Finite Speed

Type of magnet material: NdFeB

Bearing: ball-bearings

Drive line: direct-driven

Electrical data Insulation >3

kV

Drive Principal: PWM sinus, current in

phase with induced voltage Rotor position:

yes

In Table 1 the initial specification has been mentioned that

is first used in Emetor. And the result from Emetor will then be verified with FLUX2D. Using Emetor the geometry is found as like Figure.1

Figure 1. Geometry of Machine created by using Emetor

II. FEM SIMULATION This part of the paper describes the simulation of the machine using finite-element method (FEM) software called FLUX2D [2]. Figure.2 represents the FEM version of the geometry that is build up analytically in Figure 1. In FEM calculation detailed and machine calculation can be analyzed that is documented with discussions and comparisons in next few sections.

Figure 2. FEM model of same machine crated by using FLUX2D

A. Analysis and result of simulation A new path needs to be created between magnet length (lm

=1mm) and Air gap (δ=15mm) after the Rotor core diameter (Drc=1274mm) to compare this flux densities that is described in (1). Figure.3 shows the flux densities in various part of motor, rendered by different color shades. The stator tooth has higher flux densities that have been indicated with arrow-mark. This higher flux densities can be harmful for machine in cases. Such as demagnetization can be happen for magnet for this higher flux density. The flux density in several selected areas has been showed in Table 2 both from Emetor and FLUX2D. From table comparison it is noticeable the

results are quite closed in several point of the machine like air gap flux, stator yoke and rotor yoke. While in stator teeth the flux density is a bit higher yet negotiable. The next designer of the machine can take care of these minor defects.

Figure 3. A zoomed shot of flux density for a sector of machine

TABLE2. COMPARISON OF FLUX DENSITY OF DIFFERENT AREA OF MACHINE

Flux Densities Emetor FLUX2D Air Gap Flux [T] 1.219 1.269, 1.310

Stator Teeth [T] 1.533 1.610, 1.7710

Stator Yoke [T] 0.703 0.794, 0.850

Rotor Yoke [T] 0.162 1.430, 1.587

Radius of the path =Drc/2+ lm+ δ/2 (1) = (1274/2+1/2+15)mm = 652.5 mm

(a)

(b)

Figure 4. Flux density along air gap obtained with (a) Emetor [1] and

(b)FLUX2D [2] As the machine was calculated for 30 poles, the angle covered by the path is 360/30 = 12°. Radius of the path is measured first in Equation 1. And an observation walk through the air gap is measured in FLUX 2D. The result shows that the slot opening of the machine reduces flux density just before the air gap. At the same time the corner of the tooth also has higher flux density as the flux line also cover there. The comparison of two graphs as shown in Figure 4 (b) has a spike due to slot opening and slot effect that is not considered in Emetor (Figure 4a). The slot opening increases the reluctance of magnet circuit.

(a)

(b)

Figure 5. (a)Phase back-emf predicted by Emetor (b) Induced voltage over Phase B taken by FLUX2D.

From Figure.5(a) and Figure.5(b) can be compared with each other and it can be observed induced phase voltage determined by FLUX 2D has spikes while the predicted result from Emetor doesn’t have it. Once again the slotting effect makes this discrepancy.

B. Simulation to current Angle In Figure.6 electrical equivalent circuit is replaced to transient Magnetic 2D model of FLUX-software.

Figure6. equivalent electrical circuit with load for the modeled section of PMSM taken from FLUX2D. The circuit of Figure.6 itself is clearly visible as Y-Y connection for FLUX2D. So, the current equation should be like (2),(3),(4),(5). While for Emetor the torque is obtained analytically.

iA+iB+iC=0 (2) iA = imax sin ( ω t) (3) iB = imax sin ( ω t-2*pi/3) (4) iC = imax sin ( ω t-4*pi/3) (5)

(a) (b)

Figure 7. (a) Torque Result from Emetor (b)Torque at nominal condition produced in FLUX2D

The torque output from FLUX2D (Figure.7(b)) should be more sinusoidal if it would be considered as 80 points calculation instead of 40 point calculation. The rotor’s initial position was set at 13.44961° (mechanical degree) and it corresponds to the current angle at which the maximum torque is observed. The torque will be plotted as a function of rotor position.The torque for whole machine is calculated by multiplying torque with number of poles. From FEM simulation the mean value of Torque 710.3Nm for T=P*710.3=21,309 Nm. That is less than 50% of obtained torque from Emetor. So it is needed to change the geometry to obtain similar torque from Emetor. It is noticed there is difference between the output of Emetor and FLUX 2D. One of the reasons is Emetor does not consider slot opening. In this case Emetor considers in the air gap flux is equally distributed. Moreover, FLUX2D also considers saturation-effect while Emetor does not.

Furthermore, FLUX2D calculates its results considering several points and Emetor observes the outputs considering average value. Due to these reasons it is usual to get higher value of torque from Emetor comparing Flux2D.

III. IMPROVEMENT OF DESIGN AND FLUX WEAKENING CAPABILITY

The aim of this task is to investigate the constant power capability of the previous design and to improve the same machine design. And also to obtain higher torque from FLUX2D result. The result from FLUX2D and Emetor should be identical.

A. Improvement of Design on FEM (Finite Element Method) simulation

In Table 3, the comparison of two different design geometry parameters has been portrayed. With this new design it is possible to have better torque.

TABLE3. COMPARISON OF DESIGN

Input Design Parameters Previous design Current design Shaft Diameter [mm] 650 1700

Rotor core diameter [mm] 1274 2000 Air Gap Length [mm] 1 4 Outer motor diameter 1800 2700

Machine Length [mm] 1800 1100 Stator tooth width [mm] 33 100

B. Flux weakening capability From Emetor reading the flux weakening capability of the machine can be analyzed. From Emetor the found values for this calculation are (in rms): Ubase =1732 V, Ebase= 1258.6 V, Ibase= 794.5 A.

Ψn= Ψbase =Ub/ωb = 1732/ (2*pi*3.5) = 78.79 Wb (6) Ψm= Ψrated= Eb/ Ub=960.5/(2*pi*3.5) = 57.26Wb (7) Ψmn= Ψnominal= Ψrated /Ψbase = 0.726 pu (8) Ln =̀ Ψmn √(1 − Ψ mn ) = 0.46 pu (9)

Lb= Ψn/Ibase = 0.07567mH (10) L = Ln*Lb= 0.049 mH (11)

Here when Ψmn is bigger than 1/√2 or 0.71 is considered as finite maximum speed and if it is lower than it is considered as infinite maximum speed . Normalized power over speed as a function of normalized magnet-flux linkage theory [4] has been used to find out this. The results from FLUX 2D is similar in this case.

C. Torque Vs Speed The task in this part is to plot the torque-speed curve. This torque-speed curve can be divided by into two regions: constant torque and constant power. In constant torque region torque remains constant up to base speed. The torque is inversely proportional to the speed increase.

Ideal field-weakening drive characteristics can be found in [6]. This is also shown in Figure.8. Id and Iq respectively represents the current components of direct and quadrature axis. During calculation in MATLAB two different stages has been calculated . Equation (12) is used for this calculation.

T= Ψmn* In* Tb (12)

a) (b)

Figure8. Maximum torque field-weakening control strategies(a) finite maximum speed (b) infinite maximum speed [6]

Figure9. Torque VS Speed Curve The Torque vs. Speed curve is shown in Figure.9. Here it is noticeable that the torque decreases against speed and touches to x-axis due to its finite maximum speed capability.

D. Power VS Speed As the power is constant beyond the rated speed (Pout = Pb), this is called Constant Power Speed Region (CPSR) or field weakening region. The mechanical torque can be calculated by combining torque calculated before in both constant torque and constant power region. It is usually possible to keep increase the speed at a reduced power.

Figure 10. Power VS speed curve

Figure.10 shows the power vs speed curve. The constant power region remains within desired region. Here T=0 at 180 in X-axis represents finite maximum speed.

E. d-q axis current VS Speed

Figure11. d-q axis current against speed

Figure.11 shows d and q axis currents in constant torque region and during flux weakening. As expected, at rated speed, the d-axis current equal to zero. During flux weakening, negative d-axis current is introduced which counteracts the flux from the magnet.

F. Inductance with respect to current At rated speed, the current is varied in a range such that for the values above and below the rated current, corresponding stator voltage (fundamental component) is measured from FLUX 2D. Formulas that have been used for this calculation are (13),(14).

(13) [6] (14) [6]

At rated current 794.5 A, the inductance equals to 248.7mH. which is a bit higher than Emetor value. Fig .12 (a) represents maximum speed with respect to current. At rated current the maximum speed is 220rpm.How the inductance varies with stator current is shown in Figure.12(b).

(a)

(b)

Figure12. (a) Maximum speed vs. current. (b) Variation of inductance with stator current

G. Problem and possible solution

(a) (b) Figure13. Change of FLUX2D Design in stator tooth (a) Previous Design (b)

Present Design TABLE4. INPUT PARAMETERS TO REDUCE POOR QUALITY ELEMENTS

Previous Design Present Design Stator slot opening/

slot width [p.u] 0.3 0.7

Slot wedge height [mm] 3 20

Poor quality elements in FLUX 2D

0.38% 0.1%

In Figure.13 the closed view picture of the two designs is shown and that has been fixed to keep the poor quality elements near to 0.1% (Described in Table 4). It is also a significant improvement of the design.

TABLE5. FLUX DENSITIES COMPARISON OF TWO DESIGNS

Output Previous Range Current Design Flux in stator teeth 1.540 T 1.144 T Flux in stator yoke 0.736 T 1.048 T Flux in rotor yoke 0.161 T 0.915 T

Flux range 0.1~1.5T 0.9~1.1T

(a) (b)

Figure14. Machine geometry in Emetor (a) Previous design (b) Current design

Form Figure.14 the pictorial difference of the old and new design is more visible. The change of slot wedge, height and slot-opening causes significant changes of flux density in several part of machine.

IV. MAGNET WORKING POINT

A. Magnet Selection The most commercial used PM material is neodymium-ferrite-boron (Nd-Fe-B). NdFeB has very low temperature and high temperature sensitivity. It is often necessary to increase the size of magnets to avoid demagnetization at high temperatures and high currents. On the other hand, it is advantageous to use as little PM material as possible in order to reduce the cost without sacrificing the performance of the machine. [7]

The remanence flux density of the last designed machine is 1.2 T. After investigating magnet materials available from [8] Neorem 476a has been chosen. It is stated in [8] ‘‘NEOREM 400 series grades are the most cost effective alternative for standard applications’’. Other magnets like NEOREM 793a also matching with the requirement of 1.2 T remanence flux density. But NEOREM 476a has been chosen from NEOREM 400 series.

B. Magnet Material NdFeB is a rare earth alloy of Neodymium (Nd), Iron (Fe) and Boron (B). The most commercial used PM material is neodymium-ferrite-boron (Nd-Fe-B). NdFeB has very low temperature and high temperature sensitivity. It is often necessary to increase the size of magnets to avoid demagnetization at high temperatures and high currents. On the other hand, it is advantageous to use as little PM material as possible in order to reduce the cost without sacrificing the performance of the machine. [7]

C. Magnet working point The characteristics sheet of Neorem 476a magnet (with Br=1.2T) is given as in Fig.15. In Fig.15 working point at no load, nominal load and three phase short circuit will be investigated. According to specification, maximum temperature winding is 180°C. As per design outside of magnet there is airgap of 4mm which also works as insulation part. It can be assumed maximum temperature in magnet up to 150°C is acceptable.

Figure15. Typical demagnetization curves B(H) and J (H) at different

temperatures [10] To calculate the working point of magnet no load condition should be considered at first. From material characteristic sheet demagnetization curve will be used.

D. Analysis of magnet characteristics In Figure.16 three points for no load, nominal-load and short circuit conditions are plotted.

Figure16. (H,B) plotting in B-H curve for three different conditions

Magnet working point is analyzed from the results of both FLUX2D and Emetor. As the result was much similar in improved design hence in both cases here the magnet is not demagnetized.

V. FUTURE POSSIBLE DEVELOPMENTS OF EMETOR The potential of further development of Emetor is considerable. First, the models such as the iron losses could be improved. [16] Second, new models could be added as for example to calculate the cogging torque, or mechanical losses. A thermal model could also be included in Emetor. The design procedure could be modified or completed in order to give the user more flexibility in its design. Due to the slotting effect there was some changes in the curves in Figure.4, Figure.5 and Figure.7. It can also be developed by adding slotting effect. Other topologies of PM machines could be considered in Emetor. The easiest to implement from the present models is the inset PM machine. Inset PM machines have surface mounted PMs with iron interpoles that give a salient structure. The open-circuit air gap flux density could be calculated from d- and q-axis inductances should also be calculated in order to estimate the reluctance torque. Implementing other topologies with buried PM is more difficult.[16] Additional inputs are first required to describe the position of the PMs in the rotor. Besides, PMSMs with buried PMs have highly saturated iron bridges that hold the PMs in the rotor. Some effort should also be devoted to the improvement of the user interface. Designing an optimal user interface is challenging, due to the complexity of Emetor and the high number of inputs and outputs. The feedback from the users will help to continue improve this interface. Few addition in help pages and pop-ups could be completed.

VI. CONCLUSION An educational tool to design PMSM machines called Emetor and its use with verification in machine design has been presented in this paper. It allows investigating PMSM motors with inner or outer rotor and distributed or concentrated (double-layer) windings. Emetor is web-based so it is free of access through internet. The result of Emetor is verified with FEM software named FLUX2D and few possible

developments are proposed thereby in this paper. Some examples of tutorials and the results obtained during a project have been presented. The redesigning of the machine has led to better performance characteristics. But the calculation still had to find manually. That can also be developed in Emetor. The machine when analyzed for infinite or finite maximum speed showed finite maximum speed that matched with FLUX2D result. That indicated many calculation are accurate in Emetor. Another example for this is magnet working point. The magnet wasn’t demagnetized in both cases. By improving the shortcomings of Emetor it can also be used in commercial use in future.

VII. ACKNOWLEDGEMENT The authors are grateful to “Electrical Machines and Power Electronics Groups” of “Royal Institute of technology”, Stockholm, Sweden for this project.

REFERENCES [1] Emetor web based analytical tool newly developed by Royal

Institute of Technology, Stockholm. http://www.emetor.org [2] FLUX, Finite Element Method softwares crated by Cedrat group

http://www.cedrat.com [3] J. Soulard, ‘Design of Permanent Magnet Synchronous Machines’ KTH,

2010. [4] F. Meier ‘Description of rotating machine and FEM simulations using

FLUX’, 2008. [5] F. Meier and J. Soulard, “Emetor- An educational web-based design tool

for permanent magnet synchronous machine,” Proceedings of the International Conference on Electrical Machine,2008 Paper ID 866.

[6] S. Meier, ‘Normalised power against speed characteristics as function of normalized magnet-flux linkage’, KTH 2002.

[7] Chris Mi, Analytical Design of Permanent-Magnet Traction-Drive Motors, IEEE TRANSACTION ON MAGNETICS, VOL 42, NO7, 2006

[8] http://www.neorem.fi/products/permanent-magnets/ [9] http://mceproducts.com/knowledge-base/article/article-dtl.asp?id=65 [10] Neorem Magnets, a Finnish company, who manufactures sintered

NdFeB permanent magnets . [11] S.Ruohu, ‘Demagnetization of Permanent Magnets in electrical

machines’ Helsinki university of Tevhnology, 2006. [12] L Chong, R Dutta and M.F. Rahman, ‘Perfrmance comparison of

IPMSM with distributed and concentrated windings’, IEEE Trans. Ind. Appl., Vol4, pp. 1984-1988, Oct 2006

[13] F. Mier and J. Soulard, ‘‘PMSM with Non-Overlapping Concentrated Windings: Design Guidelines and Model References’’ MONACO 2009.

[14] F. Mier ‘‘Permanent-Magnet Synchronous Machines with Non-Overlapping Concentrated Windings for Low-Speed Direct-Drive Applications’’, PhD Thesis, Royal Institute of Technologyl References’’ MONACO 2009.

[15] J.Cros and P. Viarouge,‘‘Synthesis of high performance PM motor with concentrated windings.’’ IEEE Transactions on Energy Conversion, Vol.17 Issue 2, pp. 248-253

[16] Z.Q. Zhu, D. Howe and Z.P. Xia, “Prediction of open-circuit airgap field distribution in brushless machines having an inset permanent magnet rotor topology”,IEEE Trans. on Magnetics, vol. 30, no. 1, pp 98-107,1994.