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The invention relates to a permanent-magnet synchronous machine, and to a method for suppression of harmonics.
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 paper presents an analytical method for determining the harmonic content in the flux pattern of permanent magnet synchronous machines due to the slotting of the stator. The analysis based on a rotor construction with magnets radially magnetized and a retaining ring to support them against the centrifugal forces.
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.
- This paper presents an analytical method for determining the harmonic content in the flux pattern of permanent magnet synchronous machines due to the slotting of the stator. The analysis based on a rotor construction with magnets radially magnetized and a retaining ring to support them against the centrifugal forces.
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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.
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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.
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A permanent-magnet synchronous machine which is designed as shown in FIGS. 2 to 4 has, in particular, the following winding factors:| 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
Space harmonics fluxes are produced by the windings, slotting, magnetic saturation, inequalities in the air gap length. These harmonic fluxes induce voltages and circulate harmonic currents in the rotor windings. The interaction between the harmonic currents generated in the rotor and the harmonic fluxes results in the Harmonic torques, vibrations and the noise.
The air gap flux set up by the three phase stator windings carrying sinusoidal currents. The wave shape is non-sinusoidal in nature. According to Fourier series analysis, any non-sinusoidal flux is equivalent to the combination of a number of sinusoidal fluxes of fundamental and higher order harmonics. Since, the flux wave shape has half-wave symmetry, all even harmonics (2,4,6 ……) are absent in Fourier series.
A non-sinusoidal flux can be resolved into fluxes of fundamental and higher order odd harmonics (3, 5, 7, 11, 13, etc). The third harmonic flux wave produced by each of the three phases neutralizes one another. The resultant air gap flux is free from third harmonics and its multiples. This is because the third harmonics in the flux wave of all the three phases are in space phase, but differ in time phase by 120 degrees.
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A 3 phase winding carrying a sinusoidal currents produces space harmonics of the order h = 6k ± 1, where k is a positive integer (1, 2, 3…..). The synchronous speed of the hth harmonic is (1/h) times the speed of the fundamental wave. Space harmonic waves rotate in the same direction as the fundamental wave, if h = 6k + 1 and if h = 6k – 1 than it rotates in the opposite direction.
Space harmonic wave of the order h, is equivalent to a machine with the number of poles equal to (h x number of poles of the stator). Therefore, the synchronous speed of the hth space harmonic wave is
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Where,
- f = supply frequency
- P = number of poles of the stator
Thus, for the value of k = 1, a 3 phase winding will produce backward rotating fifth harmonic at the speed of (1/5) of the synchronous speed and forward rotating seventh harmonic rotating at a speed of (1/7) of the synchronous speed. These harmonics alone will have an effect on the operation of the motor.
The speed torque characteristics of the fundamental flux and the fifth and seventh space harmonic flux are shown below.
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The fifth harmonic torque opposes the fundamental component torque as the fifth harmonic flux rotates in the opposite to the rotation of the rotor. Thus, the fifth harmonic flux produces a braking torque. The seventh harmonic flux rotates in the same direction as that of the fundamental flux. Hence, the resultant torque speed characteristic will be the combination of the fundamental fifth and seventh harmonic characteristic.
The resultant torque speed characteristics have two dips, one near (1/5) of the synchronous speed and the other near (1/7) of the synchronous speed. The dip near (1/5) of the synchronous speed occurs in the negative direction of the motor rotation.
The motor will accelerate to the point L, which is the interaction between the load torque characteristic and the motor torque-speed curve. This motor torque is developed because of the fundamental flux alone. The load torque curve intersects the motor torque speed characteristics at the point A this is because of the presence of the seventh harmonics flux torque.The seventh harmonic flux torque curve has a negative slope at the point A.
The motor torque falls below the load torque. At this stage, the motor will not accelerate up to its normal speed, but will remain running at a speed which is nearly (1/7) of its normal speed, and the operating point is A. This tendency of the motor to run at a stable speed as low as one seventh of the normal speed Ns. In this condition the motor is unable to pick up its normal speed is known as crawling of the motor.
Crawling can be reduced by reducing fifth and seventh harmonics. This can be done by using a chorded or short pitched winding.