The invention relates to a permanent-magnet synchronous machine, and to a method for suppression of harmonics.
The study of the hybrid synchronous generator with skewed stator slots is performed. The skewed stator slots help to improve the line voltage wave-form and reduce the superior rank harmonics. The line voltage wave-forms obtained and the flux density for each semi-machine are presented. Key words: hybrid synchronous generator; skewed stator slots. This paper proposes a novel skewed-type iron slot wedge that can improve both the cogging torque and the output power of a permanent magnet synchronous generator (PMSG). Generally the open slot structure is adopted in a PMSG due to its convenient winding work, but the high cogging torque is undesired. Firstly, an iron slot wedge was utilized to reduce the cogging torque of an open slot type.
Permanent-magnet synchronous machines, whose rotor is excited by means of permanent magnets, have various advantages over synchronous machines with electrical excitation. For example, the rotor in a permanent-magnet synchronous machine does not require any electrical connection. Permanent magnets with a high energy density, that is to say a large product of the flux density and field strength, have been found to be superior to permanent magnets with less energy. It is also known that permanent magnets cannot only be arranged flat with respect to the air gap, but could also be positioned in a form of joint configuration (flux concentration).
Disadvantageous oscillating torques can occur in permanent-magnet synchronous machines. Skew of a rotor or of a stator in the permanent-magnet synchronous machine by, for example, one slot pitch, as is described for conventional motors in EP 0 545 060 B1, can lead to a reduction in the torque. In permanent-magnet synchronous machines with conventional winding, that is to say windings which are produced using the pulling-in technique, skew by one slot pitch is generally implemented in order to reduce cogging torques, which also lead to oscillating torques.
In permanent-magnet synchronous machines which have tooth-wound coils it is, for example, possible to reduce the oscillating torques by special shaping of the magnets. This has the disadvantage that special shaping of the magnets leads to increased production costs.
This synchronous machine also has electromotive force harmonics, depending on the winding of the stator of a three-phase permanent-magnet synchronous machine and the configuration of the rotor of this synchronous machine. These electromotive force harmonics affect the magnetic field profile in the air gap between the stator and the rotor. The electromotive force harmonics cause oscillating torques.
The invention is accordingly based on the object of specifying a permanent-magnet synchronous machine in which oscillating torques, or cogging torques, are reduced in a simple manner. This reduction is advantageously achieved without the use of any skew, for example of the permanent magnets.
The object is achieved by a method having the features as claimed in claim 1. A further solution for a permanent-magnet synchronous machine is achieved by the features as claimed in claim 3. The dependent claims 2 and 4 to 6 disclose further advantageous developments of the invention.
In a method for harmonic suppression in a permanent-magnet synchronous machine, harmonics are reduced by means of a winding configuration and by means of the magnet geometry of the permanent magnets on the rotor of the permanent-magnet synchronous machine. In this case, the permanent-magnet synchronous machine has a rotor and a stator, with the stator preferably having a three-phase winding, and the rotor having permanent magnets. The winding configuration is used to reduce the first harmonic, and the magnet geometry is used to reduce the second harmonic. The magnet geometry relates, for example, to the shape of the permanent magnets and/or to the position of the permanent magnets (for example skew of the permanent magnets), and/or to the extent of coverage of the rotor with magnetic material, that is to say with permanent magnets.
A corresponding permanent-magnet synchronous machine can be designed for a method such as this.
A permanent-magnet synchronous machine which also achieves the object according to the invention has a stator and a rotor. The stator has a three-phase winding and the rotor has permanent magnets. Furthermore, the stator has 21 teeth, and the rotor has four magnet poles.
The described embodiment makes it possible for the permanent-magnet synchronous machine to advantageously have high utilization and a high power factor. This is also the situation in particular when the permanent-magnet synchronous machine has a winding configuration as shown in FIG. 2. The permanent-magnet synchronous machine according to the invention thus allows reduced cogging torque formation, with a specific combination of a number of slots in the stator and a specific number of poles on the rotor. The reduced cogging torque formation results in particular from the winding concept. The number of poles (=the number of magnet poles) on the rotor indicates the number of useful poles. According to the invention, the number of useful poles is four.
Furthermore, there is no need for any skew and/or staggering (stepped skew) for the rotor and/or for the stator in order to reduce the cogging torques in the synchronous machine according to the invention since reduced torque ripple can be achieved just by their design. The possibility to dispense with skew and/or staggering reduces the complexity for construction of the permanent-magnet synchronous machine.
A spectrum of air gap fields can be produced by the current flow through the stator winding. On analysis of this spectrum of air gap fields, a distinction can be drawn between harmonic fields and a fundamental field over the circumference of 360 degrees.
For the permanent-magnet synchronous machine according to the invention, the number of basic pole pairs is pg=1. The number of basic pole pairs pg is defined as follows: pg is the smallest number of pole pairs resulting from the Fourier analysis of the air gap field. The number of useful pole pairs pn results from the number of pole pairs on the rotor, and is a consequence 2, since the rotor has two magnet pole pairs.
This results in use of a second harmonic for the permanent-magnet synchronous machine. The fundamental and the harmonics of a field profile in an air gap in an electrical machine may, for example, be determined by means of a Fourier analysis.
In one advantageous refinement, the winding of the stator is designed in such a manner that, in particular, disturbing harmonics such as the fifth (5 pn) and seventh (7 pn) harmonic have only a small amplitude. The fifth and the seventh harmonic are particularly disadvantageous because they have opposite rotation directions and in each case lead to torque fluctuations with the sixth harmonic, at the rotor rotation speed.
The fifth and seventh harmonic of the rotor field rotate at the rotor frequency. The stator field 5 pn rotates at ⅕ of the rotor frequency in the opposite direction to the rotor, and the stator field 7 pn rotates at 1/7 of the rotor frequency in the same direction as the rotor. The stator and rotor fields at 5 pn and 7 pn oppose one another 6 pn-times per rotor revolution, and produce a torque ripple at 6 pn per rotor revolution.
In order to reduce the fifth harmonic and the seventh harmonic, the winding, particularly in the case of synchronous machines, has until now also been short-pitched, with 18 slots. In addition, short-pitching of the winding is complex, and can be avoided in the permanent-magnet synchronous machine according to the invention.
In a further advantageous refinement of the permanent-magnet synchronous machine, its stator has 21 slots, with three slots not being wound. In one advantageous refinement of the permanent-magnet synchronous machine, the three slots that are not wound are used for cooling on the permanent-magnet synchronous machine. By way of example, a cooling medium can be passed through the slots. In one embodiment, additional cooling channels are also incorporated in the slots for this purpose. The cooling medium is either gaseous or liquid. The slots which are not wound can also be provided, for example, in order to hold a heat pipe or a cool jet, or these slots have a corresponding cooling device. The three slots are advantageously distributed symmetrically in the stator.
A further embodiment of the permanent-magnet synchronous machine according to the invention is designed in such a manner that the rotor is essentially 75% to 85% covered with magnetic material. The magnetic material is essentially that of the permanent magnets. The rotor is therefore designed such that the magnetic material coverage is 75% to 85% of the pole pitch.
In a further embodiment of the permanent-magnet synchronous machine, the winding configuration of the stator is designed in such a manner that the seventh harmonic tends virtually to zero, that is to say it is greatly reduced. With a winding configuration such as this, the stator has 21 slots, which are numbered from 1 to 21. The slots are wound for three-phase current flow, with a phase U, a phase V and a phase W. The winding coils have a first winding direction and a second winding direction, with:
- a) the slots 1, 6, 7, 11, 12 and 17 being filled with the phase U, with a first coil for the phase U in the slots 1 and 6 being formed in the first winding direction, a second coil for the phase U in the slots 7 and 11 being formed in the second winding direction, and a third coil for the phase U in the slots 12 and 17 being formed in the first winding direction, and
- b) the slots 8, 13, 14, 18, 19 and 3 being filled by means of the phase V, with a first coil for the phase V in the slots 8 and 13 being formed in the first winding direction, a second coil for the phase V in the slots 14 and 18 being formed in the second winding direction, and a third coil for the phase V in the slots 19 and 3 being formed in the first winding direction, and
- c) the slots 15, 20, 21, 4, 5 and 10 being filled by means of the phase W, with a first coil for the phase W in the slots 15 and 20 being formed in the first winding direction, a second coil for the phase W in the slots 21 and 4 being formed in the second winding direction, and a third coil for the phase W in the slots 5 and 10 being formed in the first winding direction.
The slots 2, 9 and 16 are not filled with a winding—that is to say they are unoccupied—and may, for example, be used for cooling of the permanent-magnet synchronous machine.
Since the permanent magnets on the rotor or else the slots in the stator no longer need to be skewed, this results in a large number of advantages, such as:
- there is no utilization loss resulting from the skew factor,
- expensive skewed permanent magnets can be replaced by low-cost straight permanent magnets,
- if the slots in the stator would have had to be skewed according to the prior art, lower-cost and/or faster manufacturing methods can now be used for forming the slots and for winding,
- without any skew, the manufacturing facilities for fitting permanent magnets to the rotor and/or for magnetization of magnetic raw material can be simplified,
- manufacturing can be automated more easily,
- it is easier to wind the slots in the stator, since three slots are not wound,
- sensors (for example temperature sensors) which, for example, measure the temperature can be positioned in the slots which are not wound.
In the case of the permanent-magnet synchronous machine according to the invention, in order to further improve the harmonic behavior and to additionally improve the torque ripple, measures such as skewing of the permanent magnets on the rotor and/or skewing of the windings in the stator and/or corresponding staggering and/or short-pitching of the windings can additionally be carried out. The additional use of these means can also be used to improve the permanent-magnet synchronous machine since these measures can be used to reduce further undesirable harmonics. For example, each individual method can thus be used to reduce a different harmonic, and to improve the harmonic behavior.
Furthermore, the permanent-magnet synchronous machine can be designed such that the hole number is q=7/4. The hole number q indicates over how many slots per pole the winding of a winding section is split, that is to say q is the number of slots per pole and winding section. This value for the hole number is actually of major importance in order to ensure that the least common multiple of the number of poles and the number of slots is very high.
In order to keep cogging torques of permanent magnets on the rotor with stator teeth low, the number of slots and the number of poles can be chosen such that the least common multiple is as high as possible. This is achieved by the number of pole pairs (the number of useful pole pairs) being of prime number. The number of useful pole pairs is therefore a prime number.
In a further refinement of the permanent-magnet synchronous machine, the edge areas of the permanent magnets are lowered in such a manner that this results in a larger air gap over the edges of the permanent magnets.
The combination of a plurality of measures, such as the selection of the number of poles and the selection of the number of slots which together produce little cogging (cogging torque) and the use of a specific winding configuration for suppression of the seventh harmonic, are advantageous features of the invention. Furthermore, the fifth harmonic can be suppressed by selection of an advantageous magnet geometry and/or magnet width. The fifth harmonic is suppressed not only, for example, by eighty percent pole coverage but also by means of an advantageous magnet contour. The magnet geometry affects, in particular, the coverage of the poles of the rotor with magnetic material. The winding configuration and/or the magnet geometry can also be modified so as to make it possible to suppress other harmonics than those quoted by way of example, by the modification.
The invention as well as advantageous refinements of the invention will be explained in more detail, by way of example, with reference to the drawing, in which:
FIG. 1 shows, schematically, the design of a permanent-magnet synchronous machine,
FIG. 2 shows a winding diagram,
FIG. 3 shows a laminate section for a stator which has 21 slots, with three slots not being wound, and
FIG. 4 shows magnet coverage of the pole pitch.
The illustration in FIG. 1 shows a permanent-magnet synchronous machine 51 which has a stator 3 and a rotor 5. The rotor 55 has permanent magnets 57. The stator has coils 59, with the profile of the coil 59 being shown by dashed lines within the laminated stator 53. The coil 59 forms a winding. The coils 59 form end windings 61. The permanent-magnet synchronous machine 1 is intended to drive a shaft 63.
The illustration in FIG. 2 shows a winding diagram relating to a permanent-magnet synchronous machine through which three-phase current, with three phases U, V, W, can flow. The winding diagram for the stator of the permanent-magnet synchronous machine relates to a stator which has 21 slots. The 21 slots are annotated 1 to 21. The associated rotor, which is not illustrated in FIG. 2, has four poles (magnet poles), that is to say two pole pairs. According to the winding diagram shown in FIG. 2, the stator has nine coils, with each of the phases U, V and W in FIG. 2 having three coils. The winding shown in FIG. 2 has a star point 30. Star connection is particularly advantageous when the third harmonic is not eliminated. In a situation in which the third harmonic is not important, the winding diagram can be modified in such a manner that this results in delta connection, although this is not shown. Coils are formed by the windings in the slots 1 to 21. The coils have different winding directions 44, with arrows being used to illustrate the winding directions 44. A first winding direction 41 and a second winding direction 42 are indicated in FIG. 2.
The slots 1, 6, 7, 11, 12 and 17 are filled (wound) for the phase U, with a first coil for the phase U in the slots 1 and 6 being formed in the first winding direction 41, a second coil for the phase U in the slots 7 and 11 being formed in the second winding direction 42, and a third coil for the phase U in the slots 12 and 17 being formed in the first winding direction.
The slots 8, 13, 14, 18, 19 and 3 being filled (wound) for the phase V, with a first coil for the phase V in the slots 8 and 13 being formed in the first winding direction 41, a second coil for the phase V in the slots 14 and 18 being formed in the second winding direction 42, and a third coil for the phase V in the slots 19 and 3 being formed in the first winding direction 41.
The slots 15, 20, 21, 4, 5 and 10 are filled (wound) for the phase W, with a first coil for the phase W in the slots 15 and 20 being formed in the first winding direction 41, a second coil for the phase W in the slots 21 and 4 being formed in the second winding direction 42, and a third coil for the phase W in the slots 5 and 10 being formed in the first winding direction 41.
Slots 2, 9 and 16 are not filled with any winding.
The illustration in FIG. 3 shows a laminate section 32 for a stator which has 21 slots 1 to 21, and likewise has a large number of teeth 65. The slots 2, 9 and 16 are intended to hold a cooling channel 34.
The illustration in FIG. 4 shows a cross section through the rotor 55. This illustration also shows magnet coverage 36 with a pole pitch 38. The rotor 55 has four poles 39. The poles 39 are formed by permanent magnets 57. The permanent magnets 57 are fitted on a mount 35. The mount is located on the shaft 63. In the illustration in FIG. 4, the magnet coverage 36 for each of the four poles is approximately 80% of the pole pitch 38.
A permanent-magnet synchronous machine which is designed as shown in FIGS. 2Synchronous In Education
to 4 has, in particular, the following winding factors:What Is A Synchronous Class
| P | Winding factor | |
| ξs | ||
| 0 | 0 | |
| 1 | 0.222 | Basic number of pole pairs |
| 2 | 0.968 | Useful number of pole pairs |
| 3 | 0.209 | |
| 4 | 0.132 | |
| 5 | 0.088 | |
| 6 | 0.73 | |
| 7 | 5.818 · 10−6 | |
| 8 | 0.17 | |
| 9 | 0.08 | |
| 10 | 0.357 | Fifth harmonic |
| 11 | 0.357 | |
| 12 | 0.08 | |
| 13 | 0.17 | |
| 14 | 1.164 · 10−5 | Seventh harmonic |
| 15 | 0.73 |
In this case, the first column shows the number of pole pairs p, and the second column the winding factor. The winding factor is calculated as follows:
k+1 indicates the number of occupied slots for one phase. The winding factor is the quotient of the sum of the vectorially added phase voltages, and the sum of the magnitudes of the phase voltages.
The vector ai indicates the amplitudes of the voltage vectors of the phase voltages.
The vector Φi indicates the angle of the voltage vectors, in this case with the vector wi indicating whether this is a forward conductor or a return conductor.
Amplitude:
Slot angle mechanical
Return conductor=□
In which case:
k:=5
j:=√{square root over (1)}
p:=1 . . . 15
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Rotating electrical machine designers are looking for to design high-reliability, minimum power losses, maximum power, maximum torque and low mechanical resonance vibration and noise motor. To meet the needs of electrical machine designers, Flux team started developing tools that take Skew into account in 2003. Several improvements have been made to this tool.
Skew is usually accounted for by sub-dividing the active length of the machine into several 2D slices. In the latest Skew version of Flux the post processing is directly a full 3D post-processing.
Among the advantages of Skew: minimizing harmonic content in the back EMF, reducing the cogging torque, reducing the torque ripple (the torque ripples in electrical machines are
due to several factors: space harmonics, time harmonics and cogging torque) and the average torque. In order to compare the impact of the Skew of permanent magnet on the rotor, PM motors were designed in 3D as shown in Fig.1.
Fig.1 3D modeling and schematic of classical / skew synchronous machine geometry in Flux
Cogging torque analysis withFlux
Several cogging torque minimization techniques exist for permanent magnet machines. One of the foremost ones is Skew. Cogging torque results from the interaction of the rotor permanent magnets with the stator teeth (see Fig. 2). This torque produces vibration and noise which are considered undesirable in most permanent magnet machines. The strength of the torque ripple depends on the sum of both cogging torque and synchronous torque. Hence there is interest in reducing the cogging torque.
Fig. 3 Cogging torque vs rotor position.
The period of cogging torque can be determined by:
Where LCM is the least common multiplier, Ns the number of slots and Np the number of poles.
As we can see in Fig.4 a significant reduction in the cogging torque is achieved.
Table I: Peak value of the cogging torque:
Without Skew With Skew
Cogging torque (N.m) 3e-3 1e-3
Skew angle effect
As can be seen from Fig.6 a significant reduction in the cogging torque can be achieved as the Skew angle is increased. A 34% reduction in the peak cogging torque being achieved when the Skew angle= 15C° (the number of slices in this case is 5).
Fig.5 Isolvalues of flux density at no-load
Fig. 6 Cogging torque vs rotor position for different values of Skew angle.
Back electro-motive force analysis (back EMF)
The value of the no-load voltage E0 depends on the flux produced by the magnet in the air gap and the speed of the rotor.
The Figure 8 and table II summarize the computation of the back EMF for all examples shown in the paper. They both show that the peak value of back EMF is the same for the two cases of simulation. A small difference between Skew, 3D with Skew is probably found due to end effect.
Fig.7 Isovalues of flux density at no-load computed in Flux 3D
Skewed Slots In Synchronous Machines Jackpots
Table II: Amplitude of back EMF fundamental:
Skew 3D with Skew
Back EMF fundamental 11.82 11.43
Torque and current
In this part, we are interested in calculating the torque and the current for a power supply with a converter (see Fig.9). Both simulations: Skew and 3D with Skew are supplied by the same
electrical circuit implemented in Flux environment (see Fig.9).
Fig.9 Electrical circuit in Flux
Fig. 10 and 11 show the comparison at load of the current and torque respectively between the Skew and 3D with Skew computed in Flux software.
A good agreement between the curve is observed for both current and torque.
Table III : Comparison skew and 3D at no-load
Conclusion
Synchronous Motors
Results from table III clearly indicate that the Skew allows reducing the computational solving time compared with 3D Skew and 3D modeling keeping the same result as the 3D.
By selecting an optimum Skew angle, the cogging torque can be greatly reduced. Furthermore, parametric computation can be run in the Skew to optimize the machine.
Learn more about Flux finite element electromagnetic analysis
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