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Title:
PERMANENT MAGNET SYNCHRONOUS MACHINE WITH ALIGNED RELUCTANCE AND MAGNETIC TORQUE
Document Type and Number:
WIPO Patent Application WO/2019/210429
Kind Code:
A1
Abstract:
A permanent magnet synchronous machine (PMSM) with aligned reluctance and magnetic torque is provided herein. The PMSM comprises a stator having a plurality of stator slots formed therein, each one of the plurality of state slots for supporting a stator winding. The PMSM comprises a rotor arranged to rotate relative to stator. The rotor comprises a plurality of permanent magnets. Each one of the plurality of permanent magnets is positioned adjacent a corresponding barrier provided in the rotor. Each permanent magnet is configured according to a pole arc angle. Each barrier is configured according to a barrier arc angle. The pole arc angle and the barrier arc angle are set such that a magnet torque component and a reluctance torque component of the PMSM are substantially aligned.

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Inventors:
IBRAHIM, Maged (App. 23, 3330, avenue Ridgewoo, Montreal Québec H3V 1C1, H3V 1C1, CA)
PILLAY, Pragasen (EV 4127, 1455, boulevard de Maisonneuv, Montreal Québec H3G 1M8, H3G 1M8, CA)
Application Number:
CA2019/050594
Publication Date:
November 07, 2019
Filing Date:
May 03, 2019
Export Citation:
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Assignee:
VALORBEC SOCIÉTÉ EN COMMANDITE, REPRÉSENTÉE PAR GESTION VALEO S.E.C (Bureau 230, 550, rue Sherbrooke Oues, Montreal Québec H3A 1B9, H3A 1B9, CA)
International Classes:
H02K21/12; H02K1/16; H02K1/27; H02K15/03
Attorney, Agent or Firm:
NORTON ROSE FULBRIGHT CANADA LLP S.E.N.C.R.L., S.R.L. (Suite 2500, 1 Place Ville-MarieMontréal, Québec H3B 1R1, H3B 1R1, CA)
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Claims:
What is claimed is:

1. A permanent magnet synchronous machine comprising:

a stator having a plurality of stator slots formed therein, each one of the plurality of state slots for supporting a stator winding; and

a rotor arranged to rotate relative to stator, the rotor comprising a plurality of permanent magnets, each one of the plurality of permanent magnets positioned adjacent to a corresponding barrier provided in the rotor, each permanent magnet configured according to a pole arc angle and each barrier configured according to a barrier arc angle, the pole arc angle and the barrier arc angle set such that a magnet torque component and a reluctance torque component are substantially aligned.

2. The permanent magnet synchronous machine of claim 1 , wherein each barrier has an arcuate shape from a cross-sectional perspective of the rotor.

3. The permanent magnet synchronous machine of claim 1 or 2, wherein each barrier comprises at least three edges, each one of the three edges having a concave shape.

4. The permanent magnet synchronous machine of any one of claims 1 to 3, wherein each barrier comprises a first edge extending between a first point and a second point at a perimeter of the rotor, a second edge extending between the first point and a corresponding permanent magnet, and a third edge extending between the second point and the corresponding permanent magnet.

5. The permanent magnet synchronous machine of claim 4, wherein each permanent magnet extends between a third point at the perimeter of the rotor and the corresponding barrier at a tilt angle with respect to the perimeter of the rotor.

6. The permanent magnet synchronous machine of claim 5, wherein each permanent magnet is rectangular shaped from a cross-sectional perspective of the rotor and has a length and a width.

7. The permanent magnet synchronous machine of claim 6, wherein the length, width and tilt angle of the permanent magnet are set as a function of the pole arc angle corresponding to an angle between the third point and the first point at the perimeter of the rotor.

8. The permanent magnet synchronous machine of claim 7, wherein the first point and second point are set as a function of the barrier arc angle corresponding to an angle between the first point and the second point at the perimeter of the rotor.

9. The permanent magnet synchronous machine of claim 8, wherein the barrier arc angle is set at 74.4 degrees and the pole arc angle is set at 58.5 degrees.

10. The permanent magnet synchronous machine of any one of claim 5 to 9, wherein an air gap is provided at the third point between the perimeter of the rotor and each permanent magnet.

11. The permanent magnet synchronous machine of any one of claim 1 to 10, wherein each quarter of the rotor comprises one of the plurality of permanent magnets positioned adjacent the corresponding barrier.

12. A method for producing a permanent magnet synchronous machine comprising a stator and a rotor, the method comprising:

producing the permanent magnet synchronous machine by fabricating the rotor to comprise at least one permanent magnet positioned adjacent a corresponding barrier fabricated in the rotor;

obtaining, with a computer, a direct axis of a magnet flux of the permanent magnet; determining, with the computer, inductance of the permanent magnet synchronous machine for a plurality of armature current angles;

determining, with the computer, a maximum reluctance angle at which the inductance is maximized;

determining, with the computer, a position of the direct axis and a maximum reluctance axis for a plurality of pole arc angles and barrier arc angles;

determining, with the computer, a given pole arc angle and a given barrier arc angle that obtains a shift angle, the shift angle defined by the angle between the direct axis and the maximum reluctance axis; and

positioning the permanent magnet in the rotor based on the given pole arc angle and fabricating the barrier in the rotor based on the given barrier arc angle.

13. The method of claim 12, wherein determining the inductance comprises performing a finite element analysis simulation.

14. The method of claim 12 or 13, wherein the shift angle is set at 45 degrees.

15. The method of any one of claims 12 to 14, further comprising adjusting the given pole arc angle and the give barrier arc angle to improve torque characteristics of the permanent magnet synchronous machine.

16. A method for fabricating a rotor of a permanent magnet synchronous machine, the method comprising:

obtaining a rotor body;

positioning a permanent magnet in the rotor body based on a given pole arc angle, a magnet flux of the permanent magnet having a direct axis, an inductance of the permanent magnet synchronous machine for a plurality of armature current angles being maximized at a maximum reluctance angle, a position of the direct axis and a maximum reluctance axis defining a shift angle, the given pole arc angle and a given barrier arc angle selected from a plurality of pole arc angles and barrier arc angles using the shift angle; and

fabricating a barrier in the rotor body based on the given barrier arc angle.

Description:
PERMANENT MAGNET SYNCHRONOUS MACHINE WITH ALIGNED RELUCTANCE AND

MAGNETIC TORQUE

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority to U.S. Provisional Patent Application bearing serial No. 62/666,295 filed on May 3, 2018, the contents of which are hereby incorporated by reference.

TECHNICAL FIELD

[0002] The present disclosure relates generally to permanent magnet synchronous machines and, more particularly, to the effect of reluctance torque and magnetic torque on the performance of such permanent magnet synchronous machines.

BACKGROUND OF THE ART

[0003] Synchronous machines with permanent magnets (PMSMs) (e.g., such as rare-earth magnets) are widely utilized in various applications ranging from small house appliances to large wind turbines, as they can provide higher torque density and efficiency compared to conventional brushed DC, induction and wound rotor synchronous machines.

[0004] Recently, there has been an increasing demand on rare-earth magnets, which is partly driven by the rapid growth of hybridelectric vehicles (HEV), electric vehicles (EV) and wind energy industries. There is also concern about the future availability of rare-earth elements at economical prices, as their highly concentrated production may not be able to match increasing global demand. Therefore, it is of interest to find alternative electric machine technologies that can eliminate or reduce the use of rare-earth magnets.

[0005] In a conventional interior PMSM design, the magnet torque component and the reluctance torque component reach their maximum values at different torque angles, and thus the total output torque can only utilize a portion of the reluctance torque and magnet torque. Theoretically, if one of these torque components is shifted towards the other, the total output torque utilization will be improved and lower magnet volume will be required to generate the same output torque. The reluctance torque can be shifted by adding an air gap in spaced relationship with the magnet. However, the additional air gap is found to cause a reduction in the reluctance torque magnitude, which results in a limited gain in the machine total torque. Moreover, the torque ripple in existing PMSM designs with air gaps can be severe in some cases.

[0006] As such, there is a need for improved PMSMs.

SUMMARY

[0007] In one aspect, there is provided a permanent magnet synchronous machine comprising: a stator having a plurality of stator slots formed therein, each one of the plurality of state slots for supporting a stator winding; and a rotor arranged to rotate relative to stator, the rotor comprising a plurality of permanent magnets, each one of the plurality of permanent magnets positioned adjacent a corresponding barrier provided in the rotor, each permanent magnet configured according to a pole arc angle and each barrier configured according to a barrier arc angle, the pole arc angle and the barrier arc angle set such that a magnet torque component and a reluctance torque component are substantially aligned.

[0008] In some embodiments, each barrier has an arcuate shape from a cross-sectional perspective of the rotor.

[0009] In some embodiments, each barrier comprises at least three edges, each one of the three edges having a concave shape.

[0010] In some embodiments, each barrier comprises a first edge extending between a first point and a second point at a perimeter of the rotor, a second edge extending between the first point and a corresponding permanent magnet, and a third edge extending between the second point and the corresponding permanent magnet.

[0011] In some embodiments, each permanent magnet extends between a third point at the perimeter of the rotor and the corresponding barrier at a tilt angle with respect to the perimeter of the rotor.

[0012] In some embodiments, each permanent magnet is rectangular shaped from a cross- sectional perspective of the rotor and has a length and a width. [0013] In some embodiments, the length, width and tilt angle of the permanent magnet are set as a function of a pole arc angle corresponding to an angle between the third point and the first point at the perimeter of the rotor.

[0014] In some embodiments, the first point and second point are set as a function of a barrier arc angle corresponding to an angle between the first point and the second point at the perimeter of the rotor.

[0015] In some embodiments, the barrier arc angle is set at 74.4 degrees and the pole arc angle is set at 58.5 degrees.

[0016] In some embodiments, an air gap is provided at the third point between the perimeter of the rotor and each permanent magnet.

[0017] In some embodiments, each quarter of the rotor comprises one of the plurality of permanent magnets positioned adjacent the corresponding barrier.

[0018] In one aspect, there is provided a method for producing a permanent magnet synchronous machine comprising a stator and a rotor._ The method comprises producing the permanent magnet synchronous machine by fabricating the rotor to comprise at least one permanent magnet positioned adjacent a corresponding barrier fabricated in the rotor, obtaining, with a computer, a direct axis of a magnet flux of the permanent magnet, determining, with the computer, inductance of the permanent magnet synchronous machine for a plurality of armature current angles, determining, with the computer, a maximum reluctance angle at which the inductance is maximized, determining, with the computer, a position of the direct axis and a maximum reluctance axis for a plurality of pole arc angles and barrier arc angles, determining, with the computer, a given pole arc angle and a given barrier arc angle that obtains a shift angle, the shift angle defined by the angle between the direct axis and the maximum reluctance axis, and positioning the permanent magnet in the rotor based on the given pole arc angle and fabricating the barrier in the rotor based on the given barrier arc angle.

[0019] In some embodiments, determining the inductance comprises performing an finite element analysis simulation.

[0020] In some embodiments, the shift angle is set at 45 degrees. [0021] In some embodiments, the method further comprises adjusting the given pole arc angle and the give barrier arc angle to improve torque characteristics of the permanent magnet synchronous machine.

[0022] In accordance with another embodiment of the present disclosure, there is provided a method for fabricating a rotor of a permanent magnet synchronous machine, the method comprising: obtaining a rotor body; positioning a permanent magnet in the rotor body based on a given pole arc angle, a magnet flux of the permanent magnet having a direct axis, an inductance of the permanent magnet synchronous machine for a plurality of armature current angles being maximized at a maximum reluctance angle, a position of the direct axis and a maximum reluctance axis defining a shift angle, the given pole arc angle and a given barrier arc angle selected from a plurality of pole arc angles and barrier arc angles using the shift angle; and fabricating a barrier in the rotor body based on the given barrier arc angle.

DESCRIPTION OF THE DRAWINGS

[0023] Reference is now made to the accompanying figures in which:

[0024] Figure 1 is a schematic diagram illustrating a permanent magnet synchronous machine in accordance with an illustrative embodiment;

[0025] Figure 2 is a cross-sectional partial plan view of a rotor positioned in a stator of the permanent magnet synchronous machine of Figure 1 ;

[0026] Figure 3 is a plot of torque components of an interior permanent magnet synchronous machine without aligned reluctance and magnetic torque.

[0027] Figure 4 is a flowchart illustrated an example method for aligning reluctance and magnetic torque of a permanent magnet synchronous machine in accordance with an embodiment;

[0028] Figure 5 is an exemplary plot of torque components of the permanent magnet synchronous machine of Figure 1 with aligned reluctance and magnetic torque;

[0029] Figure 6A is plot of the effect of pole arc on torque ripple and average torque in accordance with a specific and non-limiting example; [0030] Figure 6B is plot of the effect of barrier arc angle on torque ripple and average torque in accordance with a specific and non-limiting example;

[0031] Figure 6C is a plot of the effect of winding configuration on torque ripple and average torque in accordance with a specific and non-limiting example;

[0032] Figure 6D is comparison of output torque waveforms for initial and refined permanent magnet synchronous machine designs in accordance with a specific and non-limiting example; and

[0033] Figure 7 is an example computing system for implementing the method of Figure 4 in accordance with an embodiment.

[0034] It will be noted that throughout the appended drawings, like features are identified by like reference numerals.

DETAILED DESCRIPTION

[0035] Permanent magnet synchronous machines (PMSMs) with aligned reluctance and magnetic torque are described herein. Whether appropriate or not, PMSMs may also be referred to as synchronous motor.

[0036] With reference to Figure 1 , a PMSM 100 is shown in accordance with an illustrative embodiment. The PMSM 100 comprises a stator 102 and a rotor 104 arranged to rotate relative to the stator 102. The rotor 104 and the stator 102 may be made of any suitable material, for example, such as steel. In this example, the rotor 104 is adapted to be positioned internal to the stator 102, within an aperture 106 defined by a body 108 of the stator 102. This is known as an inner rotor or internal rotor configuration, in that the rotor 104 is inside the stator 102. As described hereinafter, the PMSM 100 of the present disclosure may also have an outer rotor (a.k.a., external rotor) configuration. Other types of configurations are contemplated.

[0037] With additional reference to Figure 2, the stator 102 has stator slots 110 formed therein, which carry windings, with teeth defined between each pair of slots 110. The windings are connected to an alternating current (AC) supply to produce a magnetic field. The rotor 104 comprises one or more permanent magnets 112. The permanent magnet 112 produces a magnetic field, and may be referred to as a“pole” or a“magnetic pole”. The rotor 104 may comprise a central aperture 118 shaped to mate with a rotor shaft 120. For example, the central aperture 118 may be splined, or have any other possible connector to be coupled to the rotor shaft 120. In yet another embodiment, the rotor shaft 120 is integrally formed with the rotor 104. When a current (hereinafter the“armature current”) is applied to the windings of the stator 102, a magnetic flux (hereinafter the“armature magnetic flux”) is produced. This in turn results in rotary motion of the rotor 104, with the rotational speed of the rotor 104 being as a function of the magnetic field produced by the windings. Torque is consequently generated and can be conveyed to the exterior of the PMSM 100 by the shaft 120. The permanent magnet 112 may be provided in the rotor 104 in any suitable manner, for example, by carving or cutting out the material of the rotor 104, or fabricating the rotor 104 with an area for receiving the permanent magnet 112.

[0038] A barrier 114 is provided in the rotor 104 in a spaced relationship with the permanent magnet 112, and is in the form of a gap. The barrier 114 is a flux barrier adapted to improve the utilization of torque components of the PMSM 100. The barrier 114 may be formed in the rotor 104 in any suitable manner, for example, by carving or cutting out the material of the rotor 104, or fabricating the rotor 104 with such a barrier 114. The gap defining the barrier 114 may be filled with ambient air. Alternatively, the barrier 114 may be filled of a non-magnetic and non- metal material, for example, such as resin. The configuration of the permanent magnet 112 and the barrier 114 are described in further detail elsewhere in this document.

[0039] While only a single permanent magnet 112 and a single barrier 114 are shown in Figure 2, a plurality of permanent magnets and a plurality of barriers may also be used. Each one of the plurality of permanent magnets 112 may be configured according to the permanent magnet 112 described herein. Similarly, each one of the plurality of barriers 114 may be configured according to the barrier 114 described herein. In accordance with a specific and non-limiting example of implementation, each quarter of the rotor 104 may be configured according to the embodiment shown in Figure 2, resulting in the rotor 104 having four permanent magnets and four barriers, in a barrier per magnet configuration. The number of permanent magnets and the number of barriers may vary depending on practical implementations.

[0040] In general, each permanent magnet of a PMSM has two imaginary axes, namely a d- axis and q-axis, which define a d-q rotating reference frame. The d-axis is a direct axis of a magnet flux of the permanent magnet 112 and the q-axis is a quadrature axis that is offset 90 degrees from the d-axis. In general, the electromagnetic torque of a PMSM in the d-q rotating reference frame can be represented by:

[0041] In equation 1 , P is the number of pole pairs, l is the magnet flux linkage, L d is the d-axis inductance, L q is the q-axis inductance, l s is the armature current magnitude and d is the torque angle. The total electromagnetic torque T t is composed of two components: the magnet torque component T m and the reluctance torque component T r .

[0042] With reference to Figure 3, magnet and reluctance torque components 304, 306 and corresponding total torque 302 of a convention interior PMSM, as a function of torque angle, are shown. It can be seen that the magnet torque component 304 reaches its maximum value at a torque angle of 90°, while the reluctance torque component 306 is maximized at an angle of 135°. Therefore, as the peaks of the magnet torque component 304 and of the reluctance torque component 306 are not in phase, the maximum capability of the two torque components 304, 306 at any operating condition is not fully utilized. The fundamental reason behind the partial utilization of torque components in conventional PMSMs can be explained by d-q theory as follows: the saliency of these machines is created by the magnet orientation in the rotor. This causes an axis of maximum reluctance (hereinafter the“maximum reluctance axis”) to coincide with the d-axis and an axis of minimum reluctance (hereinafter the“minimum reluctance axis”) to coincide with the q-axis. As a result, the magnet and reluctance torque components 304, 306 become zero when an armature current vector is aligned with the d-axis, and since the reluctance torque component 306 has double the frequency of the magnet torque component 304, the two components 304, 306 are maximized within 45° rotation of the armature current vector. If the maximum reluctance axis is shifted away from the d-axis, the torque component utilization will be improved given that the magnitudes of the reluctance torque and magnet torque remain constant.

[0043] In order to achieve a considerable shift between the interior PMSM torque components 304, 306 without sacrificing the reluctance torque magnitude, the rotor design shown in Figure 2 is proposed in accordance with an embodiment. Referring back to Figure 2, the barrier 114 is provided in the rotor 104 in order to guide the magnet flux away from the maximum reluctance axis. This results in the shift of the maximum reluctance axis from the d-axis, and this shift may be referred to a shift angle 0 S . The shift angle 0 S is defined by the angle between the d-axis and the maximum reluctance axis, taken from the center of the rotor 104. It should be appreciated that the magnet and reluctance torque components 304, 306 of Figure 3 would be fully utilized if the shift angle 0 S between the d-axis and the maximum reluctance axis is set to 45°.

[0044] Continuing with reference to Figure 2, the barrier 114 extends between a first point 141 and a second point 142 at the perimeter of the rotor 104. In the illustrated embodiment, the barrier 114 has an arcuate shape, from a cross-sectional perspective. In the illustrated embodiment, the barrier 114 has a first edge 151 between the two points 141 , 142, a second edge 152 between the first point 141 and the permanent magnet 112, and a third edge 153 between the second point 142 and the permanent magnet 112. In the illustrated embodiment each of the edges 151 , 152, and 153 are concave; however, the shape of the edges 151 , 152, and 153 and/or the shape of the barrier 114 may vary depending on practical implementations and may be determined by computer simulation. For example, in some embodiments, the first edge 151 is configured to be replaced with two edges configured in a V-shape. In some embodiments, the second edge 152 and/or the third edge 153 are configured to be substantially straight. Other configurations are contemplated.

[0045] The barrier 114 allows the armature magnetic flux to pass through the material of the rotor (e.g., steel) within a barrier arc angle 0 b . The barrier arc angle 0 b is defined by two radial reference lines that extend from the center of the rotor 104 to the tangentially spaced reference points 141 , 142 that the barrier 114 extends therebetween. Thus, the barrier 114 is configured in the rotor 104 according to the barrier arc angle 0 b . In the illustrated embodiment, the curved shape of the first edge 151 is configured to facilitate the flow of armature magnetic flux within the barrier arc angle 0 b of the rotor surface between the two reference points 141 , 142. The position of the maximum reluctance axis is a function of the barrier arc angle 0 b , and thus by adjusting the barrier arc angle 0 b the position of maximum reluctance axis can be set. The second edge 152 is configured to at least in part guide the magnet flux of the permanent magnet 112 to a pole arc angle 0 P (described in further detail elsewhere in this document) of the rotor surface between a third point 161 and the first point 141. Thus, in accordance with an embodiment, the second edge 152 is configured for shifting of the magnetic d-axis to the center of the pole arc angle 0 P . The third edge 153 is configured to facilitate the flow of armature magnetic flux in the direction of the minimum reluctance axis, thus increasing the reluctance torque component, as per equation (1).

[0046] The barrier arc angle 0 b may be increased or decreased by adjusting the position of the second point 142 at the rotor surface and keeping the first point 141 fixed. For example, the length of the first edge 151 can be increased and the curvature of the first edge 151 can be maintained in order to facilitate the flow of armature flux within the barrier arc angle 0 b . Accordingly, the size of the barrier 114 is a function of the barrier arc angle 0 b . In particular, the length of the barrier 114 between the two reference points 141 , 142 is a function of the barrier arc angle 0 b . Similarly, the cross-sectional area of the barrier 114, and hence the volume of the barrier 114, depends on the barrier arc angle 0 b . The lengths of the edges 151 , 152 and 153 of the barrier 114 also depend on the barrier arc angle 0 b . In accordance with an embodiment, this illustrated configuration of the barrier 114 limits a reduction in the reluctance torque magnitude and also causes a shift in the maximum reluctance axis, which leads to improved utilization of the magnet and reluctance torque components.

[0047] The permanent magnet 112 extends between the third point 161 at the perimeter of the rotor 104 and the barrier 114. In the illustrated embodiment, the permanent magnet 112 extends between the third point 161 and end points 162, 163 of the second edge 152 and the third edge 153, respectively. The end points 162, 163 of the second edge 152 and the third edge 153 are opposite of the first point 141 and the second point 152, respectively. In accordance with an embodiment, an edge 164 of the permanent magnet 112 is adjacent the third edge 153 of the barrier 114 with an angle less than 90° to prevent the permanent magnet 112 from moving during operation of the PMSM 100. In the illustrated embodiment, the tilted position of the permanent magnet 112 with respect to the rotor surface allows the magnet flux to pass through an arc of the rotor surface (between the points 161 and 141) that can be smaller in length than the length of the rectangular permanent magnet 112. This increases the fundamental component of the no-load air gap flux density, thus increasing the magnitude of the magnet torque component. Also, the position of the permanent magnet 112 allows the armature magnetic flux to flow freely below the permanent magnet 112 and the first edge 153 of the barrier 114. This increases the q-axis inductance and increases the reluctance torque magnitude. In the illustrated embodiment, the permanent magnet 112 is rectangular shaped from a cross-sectional perspective and has a length from the third point 161 to the barrier 114; however, the shape of the permanent magnet 112 may vary depending on practical implementations.

[0048] The permanent magnet 112 is configured in the rotor 104 according to the pole arc angle 0 p . The pole arc angle 0 P is the angle between the third point 161 and the first point 141 of the barrier 114 at the perimeter of the rotor 104. The pole arc angle 0 P is defined by the angle at which the magnet flux passes through the rotor surface, which in the illustrated embodiment is between the third point 161 and the first point 141. In the illustrated embodiment, the magnetic d-axis is at the center of the pole arc angle q r . Thus, the position of the magnetic d-axis is a function of the pole arc angle q r and thus by adjusting the pole arc angle q r the position of magnetic d-axis can be set. The pole arc angle q r may be adjusted by moving the third point 161 , while the first point 141 remains fixed. Also, the air gap flux density can be adjusted by changing the length and/or width of the permanent magnet 112. The variation of length, width and/or tilt angle of the permanent magnet 112 may be done while keeping the first and second points 141 , 142 fixed, so that the barrier angle 0 b would not be affected. This may result in variations in the curvature of edges 152 and 153. In accordance with an embodiment, the length, width and/or tilt angle of the permanent magnet 112 is a function of pole arc angle q r . The permanent magnet 112 is configured in the rotor 104 mainly according to the pole arc angle q r . In accordance with an embodiment, the permanent magnet 112 is configured in the rotor 104 according to the pole arc angle q r and the barrier arc angle 0 b , as the permanent magnet 112 is positioned adjacent to the barrier 114. An air gap 170 may be provided at the third point 161. The purpose of the air gap 170 is to reduce the leakage flux around the edges of the permanent magnet 112. The air gap 170 may be omitted; however, the effective air gap flux and the machine torque would typically be reduced.

[0049] With reference to Figure 4, there is shown a flowchart illustrating an example method 200 for aligning reluctance and magnetic torque of a PMSM, such as the PMSM 100 of Figures 1 and 2. At step 402, for the PMSM 100, the magnet d-axis is obtained from the air gap flux distribution at no-load. At step 404, the machine inductance is determined for different armature current angles. For example, finite element analysis (FEA) simulations may be performed for different armature current advance angles. Then, at each angle, the machine inductance is calculated. At step 406, the minimum reluctances axis and/or the maximum reluctance axis are determined from the advance angles at which the machine inductance is minimized and maximized, respectively. At step 408, the positions of the magnet d-axis and the reluctance axes (maximum reluctance axis and/or maximum reluctance axis) are determined for machines with different barrier and pole arc angles 0 b and 0 P . At step 410, the barrier and pole arc angles 0 b and 0 p that cause the desired shift angle 0 S is determined. By way of a specific and non limiting example, the PMSM 100 of Figure 2 has the desired 45° shift angle 0 S at the barrier arc angle 0 b = 74.4° and the pole arc angle 0 P = 58.8°. The barrier 114 and the permanent magnet 112 may then be configured in the rotor 104 according to the determined barrier and pole arc angles 0 b and q r . Accordingly, the method 200 may be used to produce a permanent magnet synchronous machine based on the determined barrier and pole arc angles 0 b and 0 P .

[0050] In accordance with an embodiment, the method 400 may be used for producing a permanent magnet synchronous machine 100 comprising a stator 102 and a rotor 104. The method for producing the permanent magnet synchronous machine 100 comprises producing the permanent magnet synchronous machine 100 by fabricating the rotor 104 to comprise at least one permanent magnet 112 positioned adjacent a corresponding barrier 114 fabricated in the rotor 104. The method for producing further comprises obtaining, with a computer 700, the direct axis of a magnet flux of the permanent magnet 112. The method for producing further comprises determining, with the computer 700, inductance of the permanent magnet synchronous machine 100 for a plurality of armature current angles. The method for producing further comprises determining, with the computer 700, a maximum reluctance angle at which the inductance is maximized. The method for producing further comprises determining, with the computer 700, a position of the direct axis and a maximum reluctance axis for a plurality of pole arc angles 0 P and barrier arc angles 0 b . The method for producing further comprises determining, with the computer 700, a given pole arc angle 0 P and a given barrier arc angle 0 b that obtains a shift angle 0 S , the shift angle 0 S defined by the angle between the direct axis and the maximum reluctance axis. The method for producing further comprises positioning the permanent magnet 112 in the rotor 104 based on the given pole arc angle 0 P and fabricating the barrier in the rotor 104 based on the given barrier arc angle 0 b .

[0051] With reference to Figure 5, total torque 502, magnet torque component 504 and reluctance torque component 506 are shown for the PMSM 100 configured according to the barrier arc angle 0 b and the pole arc angle 0 P as determined at step 410. For example, the magnet and reluctance torque components of the PMSM 100 configured according to the barrier arc angle 0 b and the pole arc angle, as determined by method 400, may be analyzed using the frozen permeability method to determine the total torque 502, the magnet torque component 504 and the reluctance torque component 506 shown in Figure 5. The frozen permeability method is described in M. Popescu, D. M. lonel, T. J. E. Miller, S. J. Dellinger, and M. I. McGilp, “Improved finite element computations of torque in brushless permanent magnet motors,” IEE Proceeding on Electric Power Applications, vol. 152, no. 2, pp. 271-276, Mar. 2005 and W. Q. Chu and Z. Q. Zhu,“Average torque separation in permanent magnet synchronous machines using frozen permeability,” IEEE Transactions on Magnetics, vol. 49, no. 3, pp. 1202-1210, Mar. 2013, the contents of which is hereby incorporated by reference. [0052] As illustrated in Figure 5, the magnet torque component 504 and the reluctance torque component 506 reach their maximum values at the same torque angle. Accordingly, the barrier arc angle 0 b and the pole arc angle q r of the PMSM 100 are set such that the peaks of the magnet torque component and the reluctance torque component are substantially aligned. Substantially aligned refers to the magnet torque component 504 and the reluctance torque component 506 being aligned with each other within an acceptable range (e.g., 0.1 degree, 0.5 degrees, 1 degrees, etc.; 0.1 %, 0.5 %, 1 %, 5 %, etc.). The acceptable range may vary depending on practical implementations.

[0053] It should be appreciated that by designing the barrier 114 as described herein, the PMSM 100 has, in accordance with an embodiment, a higher reluctance torque magnitude compared to the conventional inset PMSM. While the PMSM 100 has, in accordance with an embodiment, a lower magnet torque, it can still achieve the same total output torque of the conventional inset PMSM, as its torque components are fully utilized. It should further be appreciated that this allows, in accordance with an embodiment, a reduction in the magnet volume. The torque ripple of the PMSM 100 may also be reduced in comparison to the conventional inset PMSM.

[0054] Referring back to Figure 4, optionally, at step 412 the barrier and pole arc angles 0 b and O p determined at step 410 may be adjusted to improve torque characteristics. The adjustments of the barrier and pole arc angles 0 b and 0 P may be performed by computer simulation to improve torque characteristics such as torque ripple, average torque and/or any other suitable characteristics. Adjusted barrier and pole arc angles 0 b and 0 P may then be selected from the computer simulation depending on the torque characteristics sought to be improved. For example, PMSM 100 may be simulated for different pole arc angles q r that vary from the determined pole arc angles q r of step 410. The simulation results are illustrated in Figure 6A. One can see that the machine average torque increases when the pole arc is reduced, as the magnet flux is squeezed through a smaller area of rotor surface, which increases the fundamental component of the air gap flux density. It can also be seen that the average torque is maximized at a pole arc of 60°. The simulated designs with lower pole arc angles are found to have higher torque ripple and lower average torque, as the back EMF waveform deviates further from the sinusoidal waveform.

[0055] FEA simulations may be also performed for machines with different barrier arc angles 0 b that vary from the determined barrier arc angles 0 b of step 410. It can be seen from the results in Figure 6B that the barrier angle 0 b has a considerable effect on the machine average torque, as it affects the magnitude of the reluctance torque component as well as the shift angle 0 S . At a barrier angle 0 b of 80°, the machine torque ripple is minimized with only 0.68% reduction of the machine average torque.

[0056] The windings may be configured to improve torque characteristics. In some embodiments, the windings may be configured according to a fully pitched lap winding. In some embodiments, the windings may be configured according to a 1-slot short pitched winding. In some embodiments, the windings may be configured according to a 2-slot short pitched winding. The configuration of the windings may vary depending on practical implementations. The torque and the torque ripple of the PMSM 100 can be simulated for various winding configurations to determine the winding configuration to use. With reference to Figure 6C, exemplary FEA simulation results are shown for the PMSM 100 having the windings configured to each of fully pitched lap winding, the 1-slot short pitched winding and the 2-slot short pitched winding configurations. It can be seen that the 1-slot short pitched winding reduces the machine torque ripple by about 51%, due to the reduced high order back EMF harmonics. This winding configuration also reduces the machine average torque by 1.5%, as the fundamental winding factor is reduced from 0.96 to 0.945. While the 2-slot short pitching causes further reduction in the machine torque ripple, as shown in Fig. 6C, it also causes a considerable drop in the machine total torque, as its fundamental winding factor is 0.90.

[0057] From step 412, the barrier and pole arc angles 0 b and 0 P as determined at step 410 may be modified in order to improve the torque characteristics. Table 1 provides example parameters for a refined design of the PMSM 100 (as determined at step 412) from an initial design of the PMSM 100 (as determined at step 410). Figure 6D compares the output torque waveforms of the initial and the refined designs. It can be seen that the refined design led to a lower torque ripple with a slight reduction in the machine average torque.

Table 1 : Example parameters

[0058] With reference to Figure 7, the method 400 may be implemented by a computing device 700, comprising a processing unit 712 and a memory 714 which has stored therein computer- executable instructions 716. The processing unit 712 may comprise any suitable devices configured to implement the system such that instructions 716, when executed by the computing device 700 or other programmable apparatus, may cause the functions/acts/steps of the method 400 as described herein to be executed. The processing unit 712 may comprise, for example, any type of general-purpose microprocessor or microcontroller, a digital signal processing (DSP) processor, a central processing unit (CPU), an integrated circuit, a field programmable gate array (FPGA), a reconfigurable processor, other suitably programmed or programmable logic circuits, or any combination thereof.

[0059] The memory 714 may comprise any suitable known or other machine-readable storage medium. The memory 714 may comprise non-transitory computer readable storage medium, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. The memory 714 may include a suitable combination of any type of computer memory that is located either internally or externally to device, for example random-access memory (RAM), read-only memory (ROM), compact disc read-only memory (CDROM), electro-optical memory, magneto optical memory, erasable programmable read-only memory (EPROM), and electrically-erasable programmable read-only memory (EEPROM), Ferroelectric RAM (FRAM) or the like. Memory 714 may comprise any storage means (e.g., devices) suitable for retrievably storing machine- readable instructions 716 executable by processing unit 712.

[0060] The methods described herein may be implemented in a high level procedural or object oriented programming or scripting language, or a combination thereof, to communicate with or assist in the operation of a computer system, for example the computing device 700. Alternatively, the methods may be implemented in assembly or machine language. The language may be a compiled or interpreted language. Program code for implementing the methods may be stored on a storage media or a device, for example a ROM, a magnetic disk, an optical disc, a flash drive, or any other suitable storage media or device. The program code may be readable by a general or special-purpose programmable computer for configuring and operating the computer when the storage media or device is read by the computer to perform the procedures described herein. Embodiments of the methods may also be considered to be implemented by way of a non-transitory computer-readable storage medium having a computer program stored thereon. The computer program may comprise computer-readable instructions which cause a computer, or in some embodiments the processing unit 712 of the computing device 700, to operate in a specific and predefined manner to perform the functions described herein.

[0061] Computer-executable instructions may be in many forms, including program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types. Typically the functionality of the program modules may be combined or distributed as desired in various embodiments.

[0062] While embodiments of the PMSM described herein have an inner rotor and an outer stator; in alternative embodiments, the PMSM may have an outer rotor and an inner stator. For example, the outer rotor may have the permanent magnet(s) and the barrier(s) and the inner stator may have the windings.

[0063] The present disclosure may also pertain to a method for fabricating a rotor of a permanent magnet synchronous machine, the method comprising: obtaining a rotor body; positioning a permanent magnet in the rotor body based on a given pole arc angle, a magnet flux of the permanent magnet having a direct axis, an inductance of the permanent magnet synchronous machine for a plurality of armature current angles being maximized at a maximum reluctance angle, a position of the direct axis and a maximum reluctance axis defining a shift angle, the given pole arc angle and a given barrier arc angle selected from a plurality of pole arc angles and barrier arc angles using the shift angle; and fabricating a barrier in the rotor body based on the given barrier arc angle.

[0064] The above description is meant to be exemplary only, and one skilled in the art will recognize that changes may be made to the embodiments described without departing from the scope of the invention disclosed. Still other modifications which fall within the scope of the present invention will be apparent to those skilled in the art, in light of a review of this disclosure.

[0065] Various aspects of the methods, systems and PMSMs described herein may be used alone, in combination, or in a variety of arrangements not specifically discussed in the embodiments described in the foregoing and is therefore not limited in its application to the details and arrangement of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments. Although particular embodiments have been shown and described, it will be obvious to those skilled in the art that changes and modifications may be made without departing from this invention in its broader aspects. The scope of the following claims should not be limited by the embodiments set forth in the examples, but should be given the broadest reasonable interpretation consistent with the description as a whole.