CN113255281A - Fault-tolerant low-short-circuit-current double-three-phase permanent magnet motor winding design method - Google Patents
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Abstract
The invention discloses a fault-tolerant low-short-circuit-current double three-phase permanent magnet motor winding design method, and belongs to the field of motors. The invention establishes a double three-phase motor magnetomotive force and inductance performance analysis model considering the winding phase shift angle, and provides a novel double three-phase winding mutual difference 7.5-degree phase shift structure aiming at a 48-slot/22-pole permanent magnet motor based on a fault-tolerant low-short-circuit current winding orientation design method, two sets of symmetrical windings are connected in a star shape, and good electromagnetic isolation exists between each phase of magnetic lines of force, so that the motor interphase coupling effect is effectively reduced; meanwhile, the winding structure reserves certain subharmonic content through specific phase design, effectively improves the self-inductance amplitude of the motor, and basically does not influence the torque output capacity of the motor. The invention can reduce the mutual inductance of the motor and simultaneously improve the self-inductance amplitude of the motor, effectively inhibit the mutual inductance/self-inductance ratio and the short-circuit current and realize the design of the fault-tolerant low-short-circuit current motor.
Description
Technical Field
The invention relates to the field of motors, in particular to a fault-tolerant low-short-circuit-current double-three-phase permanent magnet motor winding design method. The invention is suitable for motor systems which require high reliability, such as electric automobiles, ship propulsion and the like.
Background
The permanent magnet synchronous motor has the advantages of simple structure, high power density and high efficiency, and is widely applied to the fields of full electric airplanes, electric automobiles, ship propulsion and the like. The abundant magnetomotive force and magnetic field harmonic waves of the fractional slot concentrated winding motor can generate great iron core loss and low-order electromagnetic force, so that the motor generates heat seriously and has large vibration amplitude, and the reliable operation of a permanent magnet motor system is seriously threatened. Adopt the distribution winding structure to avoid the effective means of above-mentioned risk, nevertheless compare concentrated winding structure, the distribution winding motor has the big drawback of alternate coupling, therefore provides novel low alternate coupling's winding structure and has very important theoretical meaning and practical value.
Different from the traditional three-phase winding structure, the permanent magnet motor adopts a double three-phase winding structure, and the motor winding factor can be further improved and the magnetomotive force harmonic content can be reduced through the directional design of two sets of winding magnetomotive forces, so that the motor iron loss is reduced, the motor efficiency is improved, and the permanent magnet motor becomes an effective means for improving the power density of the motor. The existing double three-phase winding structure research focuses on improving the torque performance, and the double three-phase winding mutual difference 30-degree phase shift structure can effectively improve the torque density of the motor while obviously eliminating torque pulsation. However, the existing research rarely considers the influence of the phase shift angle of the double three-phase winding on the inductive performance of the motor, neglects the problem of high phase-to-phase coupling of a 30-degree phase shift structure, increases the mutual inductance, and reduces the fault-tolerant capability of the motor; on the other hand, the 30-degree phase shift structure can reduce self inductance of the motor, so that short-circuit current of the motor is increased, and the safe operation capability of the motor is seriously damaged. Therefore, for the application fields of aerospace and other motor systems requiring high reliability, the traditional double-three-phase mutual difference 30-degree phase shift structure is difficult to meet the application requirements.
In conclusion, the traditional double three-phase winding phase shift angle design mainly aims at eliminating magnetomotive force harmonic waves and improving torque performance, neglects the influence of phase shift on self inductance and mutual inductance performance of a motor, and can cause serious motor coupling and large short-circuit current, thereby seriously threatening the operation reliability of a motor system. Therefore, in the design of the double three-phase winding structure, the inductance performance needs to be researched intensively.
Disclosure of Invention
The invention aims to overcome the defects of serious interphase coupling and large short-circuit current of a distributed winding motor, and provides a novel permanent magnet motor winding structure which can ensure the fault-tolerant performance and the low short-circuit current characteristic of the motor and basically does not sacrifice the performances of the motor such as back electromotive force, torque density, efficiency and the like.
In order to achieve the purpose, the invention adopts the technical scheme that: a fault-tolerant type low-short-circuit-current double-three-phase permanent magnet motor winding design method is characterized in that a double-three-phase winding magnetomotive force analysis model is established, and a rule between a phase shift angle and elimination of magnetomotive force harmonic waves is summarized. Based on the motor winding function theory, the contribution degree of each order of magnetomotive force harmonic to the self inductance and mutual inductance of the motor is respectively researched, the design key points of improving the self inductance of the motor and reducing the mutual inductance of the motor are clarified, and meanwhile, the electromagnetic properties of the motor, such as back electromotive force, torque and the like, are not sacrificed. The mathematical representation formula of the short-circuit current of the motor is deduced, the influence of the self-inductance amplitude on the short-circuit current of the motor is theoretically explained, and a novel double three-phase winding mutual difference 7.5-degree phase shift structure is provided, so that the self-inductance amplitude of the motor is improved while the mutual inductance of the motor is reduced, the mutual inductance/self-inductance ratio and the short-circuit current value are effectively inhibited, and the fault-tolerant low-short-circuit-current motor design is realized.
Specifically, the motor of the invention is realized by adopting the following technical scheme: a fault-tolerant type double three-phase permanent magnet motor winding design method with low short-circuit current comprises the following steps:
step 1: determining a unit motor according to the slot pole ratio of the motor, establishing a unit motor slot vector analysis model, and determining slot vector distribution of the double three-phase windings based on the principle that the fundamental wave synthetic vector is the maximum;
step 2: according to the distributed phase slot vector set of the motor, taking the A1 phase slot vector as an origin, and determining the space angle difference between the other five-phase windings and the A1 phase; based on a slot vector analysis model, establishing mathematical representation of the winding coefficient of each order harmonic of the unified double three-phase winding, and calculating to obtain the spatial content of each order harmonic;
and step 3: neglecting the notch effect of the motor, establishing a magnetomotive force analysis model considering the phase shift angle of the winding, judging the elimination rule between the phase shift angle and the magnetomotive force harmonic wave, and calculating to obtain the air gap leakage coefficient of the motor;
and 4, step 4: based on a motor winding function theory, establishing an analysis model of magnetomotive force and self-inductance characteristics, revealing the contribution degree of each order of magnetomotive force harmonic to the inductance amplitude, feeding back to the double three-phase winding phase shift angle design, determining the motor winding structure with the maximum self-inductance amplitude, establishing a short-circuit current analysis model, and revealing the relation between the inductance amplitude and the short-circuit current;
and 5: based on a motor winding function theory, the influence of double three-phase winding phase shift on a mutual inductance amplitude is disclosed, a motor mutual coupling coefficient is calculated, a two-phase winding with the highest phase coupling is identified, a phase shift angle design method for reducing the problem of phase-to-phase magnetic line coupling is searched, the reduction of the motor mutual inductance/self-inductance ratio is realized, and therefore the fault-tolerant performance of the motor is improved;
step 6: according to the change rule of the self-inductance and mutual-inductance performance of the motor along with the phase shift angle, the two three-phase winding mutual difference 7.5-degree phase shift structure is obtained in a summarizing mode, and the design of the fault-tolerant low-short-circuit-current permanent magnet motor can be achieved.
Further, in step 1, the motor slot pole ratio is 48 slots/22 poles, the number of unit motors is 1, the number of unit motor slots satisfies a multiple of 48, the motor slot pitch angle is equal to 7.5 °, and the phase shift angles which can be adopted under the slot pole ratio are determined to be 7.5 °, 15 °, 22.5 °, 30 °, 37.5 °, 45 °, and 52.5 °; the phase difference of the fundamental wave slot vectors is equal to 82.5 degrees, a unit motor slot vector star diagram is constructed according to the principle of anticlockwise rotation, 8 slot vectors of each phase are distributed according to the slot vector space position of each phase winding determined by a given phase shift angle, and the winding of the double three-phase winding is completed.
Further, the step 2) specifically comprises:
step 2.1) determining the space phase difference of the double three-phase windings:
determining the vector attribution of each phase slot according to the fundamental wave slot vector, and establishing a 1-order harmonic slot vector analysis model so as to determine the relationship between the space position angle and the phase shift between the corresponding phases of the two sets of windings as follows
In the formula, alpha represents the phase shift angle between phases corresponding to the double three-phase windings, v represents the harmonic order of the magnetomotive force, and gamma2v-γ1vV representing two sets of windingsthAngular difference of magnetomotive force harmonics;
step 2.2) establishing a mathematical representation of a double three-phase motor winding function considering a phase shift angle:
the function of each phase winding of the double three-phase motor can be expressed as
Where i denotes the three-phase winding sequence (i 1,2), NAiAs a function of the Ai phase winding, NBiAs a function of the Bi phase winding, NCiAs a function of the Ci phase winding, theta is the rotor spatial position angle, NvAnd gammaivRespectively represent vthAmplitude and phase of magnetomotive force harmonic, and Nv＝2NckwvN,/pi v, wherein kwvRepresenting the winding coefficient, NcThe general winding coefficient expression representing the number of turns of the coil is
In the formula Z0Indicating the number of slots of the unit motor.
Further, the step 3) specifically comprises:
step 3.1) establishing a double three-phase motor magnetomotive force analysis model:
the expression of the magnetomotive force of the double three-phase motor can be described as
Wherein t is time, iAi(t) is Ai phase current, iBiIs a Bi phase current, iCiThe phase current of Ci is substituted into the expression of magnetomotive force and current, and the double three-phase motor can be obtainedThe specific expression of the magnetomotive force is
In the formula, gamma1vIs the initial phase angle of magnetomotive force, gamma, of the first set of three-phase windings2vIs the initial phase angle of the magnetomotive force of the second three-phase winding setmRepresenting the maximum value of the phase current, omega the angular frequency,
step 3.2) determining the relation between the phase shift angle and the elimination of the magnetomotive force harmonic wave:
according to the magnetomotive force expression of the double three-phase motor, the magnetomotive force phase difference and the phase shift angle between the two sets of windings can be eliminated when the following formula is satisfied
In the formula [ theta ]fRepresents the phase angle of the magnetomotive force harmonic wave of forward rotation, the order of the phase angle is 6l-1, l is a natural number, and thetabThe harmonic phase angle of the magnetomotive force of the reverse rotation is shown, the order of the harmonic phase angle is 6l +1, and h is a natural number;
step 3.3) calculation of magnetic flux leakage coefficient
The leakage coefficient sigma of the double three-phase motor is calculated as
Wherein p represents the number of pole pairs of the motor, kwpThe fundamental winding coefficient is expressed, and it is worth pointing out that the eliminated magnetomotive force harmonic component should not be taken into account in the calculation of the leakage coefficient.
Further, the step 4) specifically comprises:
self-induction L of motorselfAnd magnetizing inductance LmLeakage inductance L with air gapσCan be expressed as
Lself＝Lm+Lσ＝(1+σ)Lm
For a double three-phase winding motor, the magnetizing inductance is generated by double three-phase synthetic magnetomotive force, and on the other hand, according to the motor winding function theory, the A1 phase self-inductance expression of the double three-phase motor can be written into
In the formula of0Denotes the vacuum permeability, RgDenotes the motor air gap radius,/efIndicates the effective axial length of the motor, NA1(theta) is a1 phase winding function,
the function of the air gap length of the motor is represented, and for the surface-mounted permanent magnet synchronous motor, the air gap length of the motor can be considered to be a constant value g, so that the relation between the self-inductance average value of the motor and the magnetomotive force harmonic wave can be represented as
Wherein L is0Is the self-inductance average value;
based on the generation mechanism of the magnetizing inductor, the eliminated magnetomotive force harmonic wave can not be taken into account in the calculation process of the amplitude of the inductor, and the short-circuit current expression is
In the formula, NcDelta represents the phase angle between the fault phase axis and the D axis, delta being the number of coil turns0To its initial phase angle, Ψm(0)Is the amplitude of the permanent magnet flux linkage before failure, RA1Representing the phase resistance of the machine, IRFor the purpose of its rated current value,
is the included angle between the current vector and the D axis direction.
Further, the step 5) specifically comprises:
according to the theory of motor function, taking A1 phase and A2 phase as examples, the mutual coupling coefficient m of the motorcCan be expressed as
NA2(θ) is a2 phase winding function, LA1A1Is self-induction of A1 phase, MA1A2Mutual inductance of A1 phase and A2 phase;
for a dual three-phase winding machine, the mutual inductance expressions may be described as
Wherein M isA1B1_0Is the average of the mutual inductance of A1 phase and B1 phase, MA1A2_0Is the average of the mutual inductance of A1 phase and A2, MA1B2_0Is the average of the mutual inductance of A1 phase and B2 phase, MA1C2_0The average value of the mutual feeling of the A1 phase and the C2 phase is shown.
Furthermore, the phase shift structure is a double-three-phase shift structure with a mutual difference of 7.5 degrees, the A1 phase winding coils are connected in series according to the sequence of 45-43, 45-47, 1-3, 19-21, 23-25 and 27-25, the spatial position of the A2 phase winding coil is different from that of the A1 phase winding coil by 262.5 degrees, and the connection sequence of the A2 phase winding coils can be determined to be 6-8, 10-12, 14-12, 32-30, 32-34, 36-34 and 36-38; similarly, the coil positions of the motors B1 phase, B2 phase, C1 phase and C2 phase can be determined according to the respective phase relationships. On the premise of basically not sacrificing fundamental harmonic waves, the winding structure effectively improves the self-inductance amplitude of the motor by keeping the subharmonic content, particularly 1-order harmonic wave; on the other hand, the winding structure realizes the electromagnetic decoupling of the A1 phase and the A2 phase windings with stronger coupling in space position, and obviously reduces the mutual inductance/self-inductance ratio of the motor.
The invention has the following benefits and effects:
1. the method for analyzing the motor short-circuit current and the interphase coupling degree of the double three-phase winding covering any phase shift structure is obtained, and the defect of the traditional double three-phase winding research on the relation research between the magnetomotive force and the inductance performance is filled. By adopting the armature winding structure provided by the invention, the armature magnetomotive force harmonic of the near permanent magnetic field harmonic order can be eliminated, meanwhile, the subharmonic content which plays an important role in the self-inductance amplitude of the motor is reserved, and then, the self-inductance value of the motor is increased, and the short-circuit current amplitude of the motor is reduced.
2. The novel double-three-phase shift structure with the mutual difference of 7.5 degrees, which is obtained based on the high-reliability double-three-phase winding design method provided by the invention, enables adjacent phases with the difference of 7.5 degrees in the electrical cycle to have the spatial difference of 262.5 degrees, and no coil overlapping exists between the adjacent phases, thereby realizing natural physical isolation and electromagnetic isolation, maximally inhibiting the inter-phase coupling and improving the fault-tolerant performance of the motor.
3. The novel high-reliability winding structure provided by the invention realizes the combination of the improvement of the fault-tolerant performance of the motor and the suppression of the amplitude of the short-circuit current by changing the winding mode of the armature winding after various size parameters of the motor are determined, can avoid the interference on the size design of the motor, and has robustness and universality. On the premise of basically not sacrificing fundamental harmonic waves, the winding structure effectively improves the self-inductance amplitude of the motor by keeping the subharmonic content, particularly 1-order harmonic wave; on the other hand, the winding structure realizes the electromagnetic decoupling of the A1 phase and the A2 phase windings with stronger coupling in space position, and obviously reduces the mutual inductance/self-inductance ratio of the motor.
Drawings
FIG. 1 is a cross-sectional view of an embodiment of the present invention;
FIG. 2 is a flow chart of a fault-tolerant low-short-circuit-current double three-phase permanent magnet motor winding design method of the invention;
FIG. 3 is a topological diagram of a dual three-phase winding structure according to an embodiment of the present invention;
FIG. 4 is a slot vector star diagram for a dual three-phase winding according to an embodiment of the present invention;
FIG. 5 is a connection diagram of the windings of the phases of the dual three-phase motor according to the embodiment of the present invention; (a) is A1 phase and A2 phase; (b) b1 phase and B2 phase; (c) c1 phase and C2 phase;
FIG. 6 is a diagram of the phase winding function of an embodiment of the present invention;
FIG. 7 is a schematic diagram of the phase difference of two sets of three-phase winding magnetomotive forces of the motor according to the embodiment of the invention;
FIG. 8 is a graph comparing armature magnetomotive force spectra of different winding structures of a motor according to an embodiment of the invention;
FIG. 9 is a comparison of self-inductance curves for different winding configurations of a motor in accordance with embodiments of the present invention;
FIG. 10 is a comparison of short circuit current curves for different winding configurations of a motor in accordance with an embodiment of the present invention;
FIG. 11 is a curve of steady-state current values of different winding structures of the motor according to the embodiment of the present invention along with the variation of the rotating speed;
FIG. 12 is a magnetic line distribution comparison diagram of a motor according to an embodiment of the present invention; (a) the phase-shifting structure is a double three-phase winding mutual difference 7.5-degree phase-shifting structure; (b) the structure is a double three-phase winding structure with 30-degree phase shift;
FIG. 13 is a comparison of mutual inductance curves for different winding configurations of a motor in accordance with an embodiment of the present invention;
fig. 14 is a comparison of mutual inductance/self-inductance values for different winding configurations of a motor in accordance with an embodiment of the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The invention relates to a fault-tolerant low-short-circuit-current double-three-phase permanent magnet motor winding design, wherein a sectional view of an embodiment object of the invention is shown in figure 1, in the figure, 1-48 are motor stator slot numbers, 49 is a motor stator iron core, 50 is an electronic slot opening, 51 is a rotor iron core, 52 is a pair of permanent magnets, and 53 is an air gap between a stator and a rotor; the embodiment of the invention is a 48-slot/22-pole double three-phase motor which is divided into a stator, a rotor and an air gap; the stator comprises a stator yoke part, a stator tooth part, a stator slot and an armature winding, wherein the armature slot is a flat bottom slot, and the armature winding adopts a distributed winding mode; the rotor is cylindrical, a surface embedded permanent magnet is arranged on the surface of the rotor in a groove, the permanent magnet is made of ferrite Smco32, the upper section of the surface embedded permanent magnet is arc-shaped, the lower surface of the surface embedded permanent magnet is rectangular, and the permanent magnet and the rotor iron core are mechanically fixed by a step and uniformly distributed in the circumferential direction of the rotor; the stator core and the rotor core are made of silicon steel sheets B20AT 1500.
The permanent magnet motor comprises a stator, an air gap and a rotor, wherein the air gap exists between the stator and the rotor, and the thickness of the air gap is comprehensively selected according to the size and the processing precision of the motor.
The stator comprises an armature winding, a stator tooth part, a stator yoke part and a stator slot. The stator core is formed by laminating silicon steel sheet material B20AT1500, 48 grooves are formed in the stator, and the groove type is a flat bottom groove; the armature winding adopts a distributed winding mode, rich magnetomotive force harmonic waves caused by concentrated windings are avoided, the span is 2 stator slots, the armature winding adopts a double three-phase winding structure, the current amplitudes of two sets of symmetrical three-phase windings are the same, the number of turns of the two sets of symmetrical three-phase windings is equal, the two sets of windings are connected in a star shape, two neutral points are mutually isolated, and the dimension of a driving system is reduced. The rotor structure comprises a permanent magnet and a rotor iron core, wherein the permanent magnet is Smco32, and the rotor iron core is made of high-permeability electrical iron DT 4C. The bipolar permanent magnets are magnetized in parallel, the cross-section upper surfaces of the bipolar permanent magnets are arc-shaped, the lower surfaces of the bipolar permanent magnets are rectangular, surface embedding structures are adopted between the permanent magnets and the rotor iron core, the permanent magnets are embedded into the rotor iron core, adjacent permanent magnets are mechanically fixed through a step, and circumferential and radial sliding is avoided in the rotating process of the rotor.
Further, the outer radius r of the stator of the motoroConstrained by the installation size, is a determined value, takes the motor efficiency and the short-circuit current as optimization targets, and the inner radius r of the statoriThe relation with the outer radius of the stator is ri/ro0.75; the armature winding adopts a distributed winding mode to analyze the distribution characteristics of a motor magnetic field, and the thickness h of the yoke part of the motor statorsAnd stator tooth width wsIs hs/ws1.3; stator slot opening width bs0Is an important parameter influencing the performance of the motor, gives consideration to the requirement of inhibiting the short-circuit current amplitude of the motor, and does not sacrifice the torque output of the motorOn the premise of capacity, the notch is properly reduced, which is beneficial to reducing the short-circuit current amplitude of the motor, and the opening width b of the motor slots0Is 3 mm; tooth crest height hs0Height h of slot wedges1Thickness h of permanent magnetpmThe permanent magnet has a polar arc angle thetapmThe optimization is selected according to the high reliability design requirement.
Further, after the size of the motor is determined, the method for designing the fault-tolerant type double three-phase permanent magnet motor winding with low short-circuit current is used for further reducing the inter-phase coupling of the motor and inhibiting the amplitude of the short-circuit current. Fig. 2 summarizes a flow chart of the design method of the fault-tolerant low-short-circuit-current dual three-phase permanent magnet motor winding, which is characterized by comprising the following steps:
step 1: determining a unit motor according to the slot pole ratio of the motor, establishing a unit motor slot vector analysis model, and determining slot vector distribution of the double three-phase windings based on the principle that the fundamental wave synthetic vector is the maximum;
step 2: according to the distributed phase slot vector set of the motor, taking the A1 phase slot vector as an origin, and determining the space angle difference between the other five-phase windings and the A1 phase; based on a slot vector analysis model, establishing mathematical representation of the winding coefficient of each order harmonic of the unified double three-phase winding, and calculating to obtain the spatial content of each order harmonic;
and step 3: neglecting the notch effect of the motor, establishing a magnetomotive force analysis model considering the phase shift angle of the winding, judging the elimination rule between the phase shift angle and the magnetomotive force harmonic wave, and calculating to obtain the air gap leakage coefficient of the motor;
and 4, step 4: based on a motor winding function theory, establishing an analysis model of magnetomotive force and self-inductance characteristics, revealing the contribution degree of each order of magnetomotive force harmonic to the inductance amplitude, feeding back to the double three-phase winding phase shift angle design, determining the motor winding structure with the maximum self-inductance amplitude, establishing a short-circuit current analysis model, and revealing the relation between the inductance amplitude and the short-circuit current;
and 5: based on a motor winding function theory, the influence of double three-phase winding phase shift on a mutual inductance amplitude is disclosed, a motor mutual coupling coefficient is calculated, a two-phase winding with the highest phase coupling is identified, a phase shift angle design method for reducing the problem of phase-to-phase magnetic line coupling is searched, the reduction of the motor mutual inductance/self-inductance ratio is realized, and therefore the fault-tolerant performance of the motor is improved;
step 6: according to the change rule of the self-inductance and mutual-inductance performance of the motor along with the phase shift angle, the two three-phase winding mutual difference 7.5-degree phase shift structure is obtained in a summarizing mode, and the design of the fault-tolerant low-short-circuit-current permanent magnet motor can be achieved.
Further, in step 1, the motor slot pole ratio is 48 slots/22 poles, the number of unit motors is 1, the number of unit motor slots satisfies a multiple of 48, the motor slot pitch angle is equal to 7.5 °, and it is determined that the phase shift angles that can be adopted under the slot pole ratio are 7.5 ° (fig. 3), 15 °, 22.5 °, 30 °, 37.5 °, 45 °, and 52.5 °; the phase difference of the fundamental wave slot vectors is equal to 82.5 degrees, a unit motor slot vector star diagram is constructed according to the principle of anticlockwise rotation, 8 slot vectors of each phase are distributed according to the slot vector space position of each phase winding determined by a given phase shift angle (figure 4), and double three-phase winding (figure 5) is completed.
Further, in step 2, the vector attribution of each phase slot is determined according to the fundamental slot vector, a 1-order harmonic slot vector analysis model is established, and the relationship between the spatial position angle and the phase shift of the corresponding phase of the two sets of windings can be summarized as follows
In the formula, alpha represents the phase shift angle between phases corresponding to the double three-phase windings, v represents the harmonic order of the magnetomotive force, and beta2v-β1vV representing two sets of windingsthAngular difference of magnetomotive force harmonics.
FIG. 6 depicts the function curves of the windings of each phase of a dual three-phase 7.5 degree phase-shift structure, and so on, considering the spatial phase difference between the two windings, the winding functions of each phase of a dual three-phase motor can be uniformly expressed as
Where i denotes the three-phase winding sequence (i 1,2), NAiIs an Ai phase windingFunction, NBiAs a function of the Bi phase winding, NCiAs a function of the Ci phase winding, theta is the rotor spatial position angle, NvAnd gammavRespectively represent vthHarmonic amplitude and phase, and Nv＝2Nckwv/πv，kwvRepresenting the winding coefficient, NcThe general winding coefficient expression representing the number of turns of the coil is
Further, the specific process of step 3 is: establishing a unified expression of the currents of the double three-phase motors:
in the formula ImRepresenting phase current magnitude, ω representing angular frequency, and t representing time.
The expression of the magnetomotive force of the double three-phase motor can be described as
According to the expression of the magnetomotive force and the current of the double three-phase motor, the specific expression of the magnetomotive force of the double three-phase motor can be obtained as
FIG. 7 depicts a phase difference schematic of two sets of winding magnetomotive forces for a dual three-phase, 7.5 ° phase-shifting structure, with the magnetomotive force curves for the remaining phase-shifting structures being comparable in such ratio. Obviously, due to the magnetic potential phase compensation mechanism between the two sets of windings, according to the magnetomotive force expression of the double three-phase motor, the magnetic potential difference and the phase shift angle between the two sets of windings can be eliminated when the following formula is met
In the formula [ theta ]fRepresents the phase angle of the magnetomotive force harmonic wave of forward rotation, the order of which is 6l-1(l is a natural number), thetabThe harmonic phase angle of the magnetomotive force of the reverse rotation is shown, the order of the harmonic phase angle is 6l +1, and h is a natural number. FIG. 8 illustrates magnetomotive force spectra of a dual three-phase 7.5 ° phase-shifted structure compared to a conventional three-phase winding structure, which achieves a 13 ° phase compensation by virtue of two sets of windingsth、35th、47thThe equal-order magnetomotive force harmonic wave is eliminated, and the content of the motor magnetomotive force fundamental wave is improved to a certain extent. Based on the motor magnetomotive force analysis result, the leakage magnetic coefficient sigma of the double three-phase motor is calculated as
Wherein p represents the number of pole pairs of the motor, kwpThe fundamental winding coefficient is expressed, and it is worth pointing out that the eliminated magnetomotive force harmonic component should not be taken into account in the calculation of the leakage coefficient.
Further, the specific process of step 4 is: self-induction L of motorselfAnd magnetizing inductance LmLeakage inductance L with air gapσCan be expressed as
Lself＝Lm+Lσ＝(1+σ)Lm
For a double three-phase winding motor, the magnetizing inductance of the motor is generated by double three-phase synthetic magnetomotive force. On the other hand, according to the motor winding function theory, the double three-phase motor A1 phase self-inductance expression can be written as
In the formula of0Denotes the vacuum permeability, RgDenotes the motor air gap radius,/efThe effective axial length of the motor is shown,
the motor air gap length is expressed as a function, and for the surface-mounted permanent magnet synchronous motor, the motor air gap length can be regarded as a constant value g. Therefore, the relationship between the self-inductance average value of the motor and the magnetomotive force harmonic can be expressed as
Based on the generation mechanism of the magnetizing inductance, the eliminated magnetomotive force harmonic will not be taken into account in the inductance amplitude calculation process.
Short circuit current is expressed as
Where δ represents the phase angle between the faulted phase axis and the D axis, δ0Is its initial phase angle. Ψm(0)Is the amplitude of the permanent magnet flux linkage before failure, RA1Representing the phase resistance of the machine, IRFor the purpose of its rated current value,
is the included angle between the current vector and the D axis direction.
Further, the specific process of step 5 is: according to the theory of motor function, taking A1 phase and A2 phase as examples, the mutual coupling coefficient m of the motorcCan be expressed as
For a dual three-phase winding machine, the mutual inductance expressions may be described as
Further, the specific process of step 6.1 is: comparing and summarizing self-inductance and mutual inductance values of the motor with any feasible phase shift structure, comparing self-inductance curves of a traditional double-triphase mutual difference 30-degree phase shift structure and a novel double-triphase mutual difference 7.5-degree phase shift structure as shown in fig. 9, wherein the self-inductance amplitude of the motor is effectively improved by 9.5% through the winding structure; FIG. 10 is a comparison of short-circuit current curves of two different phase shift structures at a rated rotation speed of 200r/min, wherein the suppression effect of the winding structure of the present invention on short-circuit current reaches 13.5% no matter at a transient short-circuit current value or a steady-state current value; fig. 11 is a curve of the steady-state short-circuit current amplitude varying with the rotation speed, and it can be seen that the short-circuit current amplitude of the winding structure of the present invention is smaller than that of the conventional dual three-phase 30 ° phase shift structure in the full speed domain, and the short-circuit current suppression effect is obvious as the rotation speed increases.
The specific process of the step 6.2 is as follows: the double three-phase motor A1 phase and A2 phase windings have high electromagnetic coupling, a diagram in figure 12 shows the magnetic force line distribution patterns of A1 phase and A2 phase of a double three-phase mutual difference 30-degree phase shift structure and a novel double three-phase mutual difference 7.5-degree phase shift structure, the winding structure realizes the electromagnetic decoupling of A1 phase and A2 phase windings, no coil overlapping exists between the two phase windings, the motor mutual inductance is remarkably reduced, and as shown in figure 13, the mutual inductances of the other phases except the A1 phase and A2 phase are compared together. FIG. 14 compares the principal coupling coefficients M of a dual three-phase motorA1A2/LA1A1And MA1B2/LA1A1Compared with a double three-phase winding mutual difference 30-degree phase shift structure, the winding structure has an obvious inhibiting effect on the mutual coupling coefficient, the inter-phase coupling of the motor is improved, and the fault tolerance performance is obviously improved.
In conclusion, the invention provides a fault-tolerant type low-short-circuit-current double three-phase permanent magnet motor winding design method. The method comprises the steps of judging the elimination rule between a phase shift angle and magnetomotive force harmonic by establishing a double three-phase motor magnetomotive force analysis model considering the winding phase shift angle, then establishing an analysis model of magnetomotive force and inductive performance based on a motor winding function theory, clarifying the contribution degree of each order magnetomotive force harmonic to an inductance amplitude, feeding back to the double three-phase winding phase shift angle design, and determining a novel double three-phase winding mutual difference 7.5-degree phase shift structure. Compared with the traditional double-three-phase 30-degree phase shift structure, the winding structure has the advantages that the self-inductance amplitude of the motor is effectively improved, and meanwhile, the mutual inductance component of the motor is obviously reduced. Through the promotion to motor self-inductance amplitude, motor short circuit current amplitude is restrained, and mutual inductance's reduction has then reduced motor interphase coupling degree, has promoted the reliability of motor. The winding topological structure provided by the invention is not bound by the type of a rotor, a surface-mounted structure, a Halbach array or a built-in structure can be adopted, the purposes of improving reliability and inhibiting short-circuit current are realized by adjusting the winding structure, the sensitivity to the size of a motor is low, and the portability is strong. The invention analyzes the influence of the double three-phase mutual difference 7.5-degree winding structure on the inductive performance of the motor for the first time, and the provided scheme can provide reference research for the design scheme of the high-reliability motor winding.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (7)
1. A fault-tolerant type low-short-circuit-current double three-phase permanent magnet motor winding design method is characterized by comprising the following steps of:
step 1: determining a unit motor according to the slot pole ratio of the motor, establishing a unit motor slot vector analysis model, and determining slot vector distribution of the double three-phase windings based on the principle that the fundamental wave synthetic vector is the maximum;
step 2: according to the distributed phase slot vector set of the motor, taking the A1 phase slot vector as an origin, and determining the space angle difference between the other five-phase windings and the A1 phase; based on a slot vector analysis model, establishing mathematical representation of the winding coefficient of each order harmonic of the unified double three-phase winding, and calculating to obtain the spatial content of each order harmonic;
and step 3: neglecting the notch effect of the motor, establishing a magnetomotive force analysis model considering the phase shift angle of the winding, judging the elimination rule between the phase shift angle and the magnetomotive force harmonic wave, and calculating to obtain the air gap leakage coefficient of the motor;
and 4, step 4: based on a motor winding function theory, establishing an analysis model of magnetomotive force and self-inductance characteristics, revealing the contribution degree of each order of magnetomotive force harmonic to the inductance amplitude, feeding back to the double three-phase winding phase shift angle design, determining the motor winding structure with the maximum self-inductance amplitude, establishing a short-circuit current analysis model, and revealing the relation between the inductance amplitude and the short-circuit current;
and 5: based on a motor winding function theory, the influence of double three-phase winding phase shift on a mutual inductance amplitude is disclosed, a motor mutual coupling coefficient is calculated, a two-phase winding with the highest phase coupling is identified, a phase shift angle design method for reducing the problem of phase-to-phase magnetic line coupling is searched, the reduction of the motor mutual inductance/self-inductance ratio is realized, and therefore the fault-tolerant performance of the motor is improved;
step 6: according to the change rule of the self-inductance and mutual-inductance performance of the motor along with the phase shift angle, a phase shift structure with the minimum interphase coupling and the maximum self-inductance amplitude of the double three-phase winding motor is obtained in a summarizing mode, and the design of the fault-tolerant low-short-circuit-current permanent magnet motor winding structure is completed.
2. The method for designing the fault-tolerant low-short-circuit-current double-three-phase permanent magnet motor winding according to claim 1, wherein the step 1) specifically comprises the following steps:
the motor slot pole ratio is 48 slots/22 poles, the number of unit motors is 1, the number of unit motor slots meets the multiple of 48, the motor slot pitch angle is equal to 7.5 degrees, and the phase shift angles which can be adopted under the slot pole ratio are determined to be 7.5 degrees, 15 degrees, 22.5 degrees, 30 degrees, 37.5 degrees, 45 degrees and 52.5 degrees; the phase difference of the fundamental wave slot vectors is equal to 82.5 degrees, a unit motor slot vector star diagram is constructed according to the principle of anticlockwise rotation, 8 slot vectors of each phase are distributed according to the slot vector space position of each phase winding determined by a given phase shift angle, and the winding of the double three-phase winding is completed.
3. The method for designing the fault-tolerant low-short-circuit-current double-three-phase permanent magnet motor winding according to claim 1, wherein the step 2) specifically comprises the following steps:
step 2.1) determining the space phase difference of the double three-phase windings:
determining the vector attribution of each phase slot according to the fundamental wave slot vector, and establishing a 1-order harmonic slot vector analysis model so as to determine the relationship between the space position angle and the phase shift between the corresponding phases of the two sets of windings as follows
In the formula, alpha represents the phase shift angle between phases corresponding to the double three-phase windings, v represents the harmonic order of the magnetomotive force, and gamma2v-γ1vV representing two sets of windingsthAngular difference of magnetomotive force harmonics;
step 2.2) establishing a mathematical representation of a double three-phase motor winding function considering a phase shift angle:
the function of each phase winding of the double three-phase motor can be expressed as
Where i denotes the three-phase winding sequence (i 1,2), NAiAs a function of the Ai phase winding, NBiAs a function of the Bi phase winding, NCiAs a function of the Ci phase winding, theta is the rotor spatial position angle, NvAnd gammaivRespectively represent vthAmplitude and phase of magnetomotive force harmonic, and Nv＝2NckwvN,/pi v, wherein kwvRepresenting the winding coefficient, NcThe general winding coefficient expression representing the number of turns of the coil is
In the formula Z0Indicating the number of slots of the unit motor.
4. The method for designing a fault-tolerant low-short-circuit-current dual-three-phase permanent magnet motor winding according to claim 3, wherein the step 3) specifically comprises the following steps:
step 3.1) establishing a double three-phase motor magnetomotive force analysis model:
the expression of the magnetomotive force of the double three-phase motor can be described as
Wherein t is time, iAi(t) is Ai phase current, iBiIs a Bi phase current, iCiThe Ci phase current is substituted into the magnetomotive force and current expression, and the specific expression of the magnetomotive force of the double three-phase motor can be obtained as
In the formula, gamma1vIs the initial phase angle of magnetomotive force, gamma, of the first set of three-phase windings2vIs the initial phase angle of the magnetomotive force of the second three-phase winding setmRepresenting the maximum value of the phase current, omega the angular frequency,
step 3.2) determining the relation between the phase shift angle and the elimination of the magnetomotive force harmonic wave:
according to the magnetomotive force expression of the double three-phase motor, the magnetomotive force phase difference and the phase shift angle between the two sets of windings can be eliminated when the following formula is satisfied
In the formula [ theta ]fRepresents the phase angle of the magnetomotive force harmonic wave of forward rotation, the order of the phase angle is 6l-1, l is a natural number, and thetabThe harmonic phase angle of the magnetomotive force of the reverse rotation is shown, the order of the harmonic phase angle is 6l +1, and h is a natural number;
step 3.3) calculation of magnetic flux leakage coefficient
The leakage coefficient sigma of the double three-phase motor is calculated as
Wherein p represents the number of pole pairs of the motor, kwpThe fundamental winding coefficient is expressed, and it is worth pointing out that the eliminated magnetomotive force harmonic component should not be taken into account in the calculation of the leakage coefficient.
5. The method for designing a fault-tolerant low-short-circuit-current dual-three-phase permanent magnet motor winding according to claim 4, wherein the step 4) specifically comprises the following steps:
self-induction L of motorselfAnd magnetizing inductance LmLeakage inductance L with air gapσCan be expressed as
Lself＝Lm+Lσ＝(1+σ)Lm
For a double three-phase winding motor, the magnetizing inductance is generated by double three-phase synthetic magnetomotive force, and on the other hand, according to the motor winding function theory, the A1 phase self-inductance expression of the double three-phase motor can be written into
In the formula of0Denotes the vacuum permeability, RgDenotes the motor air gap radius,/efIndicates the effective axial length of the motor, NA1(theta) is a1 phase winding function,
expressing the function of the air gap length of the motor, for the surface-mounted permanent magnetIn the case of a synchronous motor, the air gap length of the motor can be regarded as a constant value g, so that the relation between the self-inductance average value of the motor and the magnetomotive force harmonic can be expressed as
Wherein L is0Is the self-inductance average value;
based on the generation mechanism of the magnetizing inductor, the eliminated magnetomotive force harmonic wave can not be taken into account in the calculation process of the amplitude of the inductor, and the short-circuit current expression is
In the formula, NcDelta represents the phase angle between the fault phase axis and the D axis, delta being the number of coil turns0To its initial phase angle, Ψm(0)Is the amplitude of the permanent magnet flux linkage before failure, RA1Representing the phase resistance of the machine, IRFor the purpose of its rated current value,
is the included angle between the current vector and the D axis direction.
6. The method for designing a fault-tolerant low-short-circuit-current dual-three-phase permanent magnet motor winding according to claim 1, wherein the step 5) specifically comprises the following steps:
according to the theory of motor function, taking A1 phase and A2 phase as examples, the mutual coupling coefficient m of the motorcCan be expressed as
NA2(θ) is a2 phase winding function, LA1A1Is self-induction of A1 phase, MA1A2Mutual inductance of A1 phase and A2 phase;
for a dual three-phase winding machine, the mutual inductance expressions may be described as
Wherein M isA1B1_0Is the average of the mutual inductance of A1 phase and B1 phase, MA1A2_0Is the average of the mutual inductance of A1 phase and A2, MA1B2_0Is the average of the mutual inductance of A1 phase and B2 phase, MA1C2_0The average value of the mutual feeling of the A1 phase and the C2 phase is shown.
7. The method for designing the windings of the fault-tolerant dual-three-phase permanent magnet motor with low short-circuit current according to claim 1, wherein the phase shift structure is a dual-three-phase shift structure with a mutual difference of 7.5 degrees, the winding coils of the A1 phases are connected in series according to a sequence of 45-43, 45-47, 1-3, 19-21, 23-25 and 27-25, the spatial position of the winding coil of the A2 phase is different from that of the winding coil of the A1 phase by 262.5 degrees, and the connection sequence of the winding coils of the A2 phase can be determined to be 6-8, 10-12, 14-12, 32-30, 32-34, 36-34 and 36-38; similarly, the coil positions of the motors B1 phase, B2 phase, C1 phase and C2 phase can be determined according to the respective phase relationships.
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