CN114142640A - Surface-mounted modulation magnetic pole structure design method based on specific harmonic elimination method - Google Patents
Surface-mounted modulation magnetic pole structure design method based on specific harmonic elimination method Download PDFInfo
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Abstract
The invention relates to a surface-mounted modulation magnetic pole structure design method based on a specific harmonic elimination method, which comprises the following steps: deducing a magnetic pole specific harmonic elimination principle to obtain an amplitude expression of each harmonic in a modulated magnetic pole profile waveform; designing and solving an equivalent sinusoidal magnetic pole structure of the motor according to the amplitude expression of each subharmonic; designing and solving an equivalent third harmonic injection type magnetic pole structure of the motor according to the amplitude expression of each subharmonic; simulation verification: and (3) carrying out simulation verification on the double three-phase permanent magnet synchronous motor provided with the equivalent sinusoidal magnetic pole model designed and solved in the step (2) and the equivalent third harmonic injection magnetic pole model designed and solved in the step (3). The invention can effectively improve the performance of the surface-mounted double three-phase permanent magnet synchronous motor and reduce the difficulty of processing the special-shaped outer contour by the harmonic-wave pole-cutting type magnetic pole structure.
Description
Technical Field
The invention belongs to the field of motor optimization design, and particularly relates to a technology for reducing air gap flux density harmonic waves and improving air gap flux density sine degree, which can be used for reducing motor torque fluctuation.
Background
The surface-mounted permanent magnet synchronous motor is widely applied to various fields due to simple structure and small magnetic flux leakage. At present, the requirements of various industrial application fields on the performance of a permanent magnet motor are continuously improved, and how to design a high-performance permanent magnet synchronous motor with high torque density and low torque fluctuation is a research focus and a difficulty in the field of current motor design. The performance of the permanent magnet motor such as electromagnetic torque, torque fluctuation, vibration noise and the like is closely related to the air gap flux density and the waveform sine degree, a rotor magnetic pole of the traditional surface-mounted permanent magnet motor is generally formed by arranging a whole magnetic pole according to a specified pole arc coefficient, the sine degree of the generated air gap magnetic field is poor, and various non-working subharmonics are contained, so that how to reduce the non-working subharmonics in the air gap flux density waveform has important influence on effectively reducing the torque fluctuation and the loss of the motor.
In recent years, a large amount of research is carried out by domestic and foreign scholars aiming at the optimal design of the magnetic pole structure of the surface-mounted permanent magnet motor, and a method for combining equal-width segmented magnetic poles and magnetic pole materials with different magnetization intensities is provided by scholars, so that the sine degree of the air gap magnetic density waveform is improved, but the difference of magnetic polarity energy among different materials is large, and the processing and manufacturing difficulty is increased; for the method for eccentrically cutting the outer pole arc of the rotor magnetic pole, a simple model is used for deducing a magnetic pole structure corresponding to the sinusoidal air gap flux density, and the air gap flux density harmonic wave and the cogging torque can be weakened by optimizing key parameters such as the eccentricity and the like; for the method that the magnetic pole is cut into a sine magnetic pole structure, the optimal air gap flux density waveform can be found by adjusting the edge thickness of the permanent magnet, so that the cogging torque of the motor is reduced; although the sine magnetic pole structure can make the sine degree of the air gap flux density waveform of the motor higher and effectively reduce the torque fluctuation of the motor, the production and processing of the magnetic pole are greatly difficult due to the special shape of the arc of the outer contour of the magnetic pole.
The specific harmonic elimination modulation method is proposed in 1973 by Patel H.S. and Hoft R.G. and the like, and is mainly applied to the field of variable frequency power supplies. When in useWhen the three-level inverter is applied to the driving field of a high-power motor, in order to reduce the switching frequency of a power device and further reduce the switching loss, a Specific Harmonic Elimination Technology (SHET) is adopted to eliminate low-order harmonics existing in the output voltage waveform, so that the current pulsation is reduced, and the performance of a variable frequency power supply is improved[1-2]。
The main principle of the specific harmonic elimination modulation technology is that a Fourier series model of three-phase inverter output phase voltage is utilized, the amplitude of specific subharmonic to be eliminated is set to be zero as constraint, a nonlinear transcendental equation set with a switching angle alpha as an unknown number is further solved, and finally the specific harmonic in the inverter output voltage is eliminated through modulation[3]。
Reference documents:
[1]Patel H S,Hoft R G.Generalized Techniques of Harmonic Elimination and Voltage Control in Thyristor Inverters:Part I--Harmonic Elimination[J].IEEE Trans,1973,9(3):310-317.
[2] patel, Hasmoukh, S, et al, Generalized Techniques of Harmonic amplification and Voltage Control in the resonator Inverters Part II-Voltage Control Techniques [ J ]. Industry Applications, IEEE Transactions on,1974.
[3] Analysis and control of residual harmonics in Weiyuanzhi, specific harmonic elimination technology [ D ]. Harbin engineering university, 2019.
Disclosure of Invention
The invention provides a novel surface-mounted modulated magnetic pole structure design method, which is based on the technical principle of specific harmonic elimination, utilizes a Fourier series model of modulated magnetic pole profile waveform, takes the amplitude of specific subharmonics to be eliminated or injected as constraint, solves a nonlinear transcendental equation with the initial position angle of the modulated magnetic pole as an unknown number, obtains the initial position angle of the modulated magnetic pole, and further obtains a rotor structure of the whole modulated magnetic pole by utilizing symmetry, thereby realizing the elimination and injection of specific harmonics of a motor air gap field, effectively improving the performance of a surface-mounted double three-phase permanent magnet synchronous motor, and reducing the difficulty of processing a special-shaped outer contour by a harmonic pole-cutting type magnetic pole structure. The technical scheme is as follows:
a surface-mounted modulation magnetic pole structure design method based on a specific harmonic elimination method comprises the following steps:
(1) deducing a magnetic pole specific harmonic elimination principle to obtain an amplitude expression of each harmonic in a modulated magnetic pole profile waveform;
(2) designing and solving an equivalent sinusoidal magnetic pole structure of the motor according to the amplitude expression of each subharmonic;
(3) designing and solving an equivalent third harmonic injection type magnetic pole structure of the motor according to the amplitude expression of each subharmonic;
(4) simulation verification: carrying out simulation verification on the double three-phase permanent magnet synchronous motor provided with the equivalent sinusoidal magnetic pole model designed and solved in the step (2) and the equivalent third harmonic injection magnetic pole model designed and solved in the step (3), wherein in addition to the sine current, the third harmonic current is injected into the winding, so that the third harmonic current interacts with the third harmonic in the air gap flux density to improve the electromagnetic torque; and carrying out finite element simulation and verification with the traditional surface-mounted magnetic pole structure motor.
Wherein, the method of step (1) can be as follows:
1) applying Specific Harmonic Elimination Technology (SHET) to the design process of the surface-mounted rotor magnetic pole to obtain a pair of under-pole modulated magnetic pole profile waveforms h0The Fourier series expansion expression of (1);
2) because the magnetic fields generated by a pair of magnetic poles in a period of 2 pi are in odd symmetry with the pi point, and when the modulation magnetic poles are designed, the magnetic poles of the N pole and the S pole are respectively divided into a plurality of blocks, so that the magnetic blocks under one pole are in symmetry with pi/2 in the interval of [0, pi ], even harmonics in the profile waveform of the modulation magnetic poles can be eliminated, cosine term harmonics can be eliminated, and further, the amplitude expression of each harmonic in the profile waveform of the modulation magnetic poles is obtained.
The expression of each harmonic amplitude in the modulated magnetic pole profile waveform obtained in the step (1) is as follows:
in the formula (I), the compound is shown in the specification,n (n ═ 1,3,5,7 …) is the order of each harmonic; omega is angular velocity; t is time, h is pole height, alphai(i is 1,2,3 … N) is the initial position angle of each magnetic pole in a quarter period, and should satisfy 0<α1<α2<α3…<αN<Pi/2, the initial position angle of each magnetic pole is solved, the width and the relative position of each modulated magnetic pole under a pair of poles can be solved according to the symmetry, and the whole rotor magnetic pole structure is obtained; let N number of alpha within a quarter periodiInitial position angle, eliminating (N-1) specific subharmonics.
The method in step (2) may be as follows:
1) solving the equivalent sinusoidal magnetic pole structure of the motor: the method comprises the steps that low-order harmonics which have large influence on air gap flux density sine degree are written in a column mode by using amplitude expressions of each-order harmonic in modulated magnetic pole profile waveforms, then amplitudes of other-order harmonics except fundamental waves are set to be 0, and a first nonlinear equation set consisting of the amplitude expressions of each-order harmonic is obtained;
2) solving the first nonlinear equation system to obtain the position angle of each magnetic pole: magnetic pole position angle alpha is obtained by utilizing impulse equality principleiAnd according to the calculated alphaiAnd (4) carrying out iterative solution on the initial value, and obtaining an approximate true solution of the nonlinear transcendental equation set when the program is converged to obtain the magnetic pole structure and the distribution position so as to further obtain the rotor structure.
The iterative solution of the first nonlinear equation set can adopt a Newton iterative method, and can be based on the solved alphaiAnd performing iterative solution by using the initial value as the initial value of the Matlab fslove solution function.
The method in step (3) may be as follows:
1) solving an equivalent third harmonic injection type magnetic pole structure: the low-order harmonic with large influence on the air gap flux density sine degree is written in a column mode by using the amplitude expression of each-order harmonic in the modulated magnetic pole profile waveform, then the amplitudes of other-order harmonics except the fundamental wave and the third harmonic are set to be 0, and a second nonlinear equation set consisting of the amplitude expressions of each-order harmonic is obtained;
2) solving the second nonlinear equation set to obtain each blockMagnetic pole position angle: magnetic pole position angle alpha is obtained by utilizing impulse equality principleiAnd according to the calculated alphaiAnd performing iterative solution by using the initial value as the initial value of the Matlab fslove solution function, wherein the basic iterative principle is a Newton iterative method, and when a program is converged, the approximate true solution of the nonlinear transcendental equation set can be obtained to obtain the magnetic pole structure and the distribution position, so that the whole rotor magnetic pole structure is obtained according to the symmetry.
Performing iterative solution on the second nonlinear equation set by adopting a Newton iterative method; can be based on the alpha soughtiAnd performing iterative solution by using the initial value as the initial value of the Matlab fslove solution function.
In the step (4), in order to ensure that the current amplitudes before and after the harmonic injection are the same, so as to realize that the current peak value does not exceed the current limit value of the inverter power supply, the optimal value of the current amplitude of the injected third harmonic is 1/6 of the fundamental wave amplitude.
The invention provides a novel surface-mounted modulation magnetic pole structure design method based on a specific harmonic elimination technical principle, and provides a method for calculating the number, size and position of modulation magnetic poles. The method aims to solve the width and position angle of a magnetic pole by using a specific harmonic elimination technology and realize elimination and injection of specific harmonic waves of a motor no-load air gap magnetic field. Finite element analysis results show that the novel magnetic pole structure design method provided by the invention realizes the improvement of the sine degree of the air gap flux density waveform, effectively reduces the content of non-working subharmonic in the air gap flux density, and effectively reduces the torque fluctuation of the motor. Meanwhile, the novel magnetic pole structure design method also realizes 3-order harmonic injection of the air gap magnetic field, further improves the torque density of the motor on the basis of not deteriorating the torque fluctuation of the motor, and provides an idea for designing the permanent magnet synchronous motor with high torque density and low torque fluctuation.
Drawings
Fig. 1 is a theoretical waveform diagram of modulated magnetic poles and sinusoidal magnetic poles.
Fig. 2 is a diagram of a no-load air gap flux density harmonic distribution of a conventional 10-pole 12-slot motor.
Fig. 3 is a theoretical waveform diagram of modulated magnetic poles and sinusoidal magnetic poles.
Fig. 4 is a theoretical waveform diagram of a modulated pole and a 3rd harmonic injection pole.
Fig. 5(a) is a model diagram of a conventional 10-pole 12-slot surface-mounted magnetic pole motor.
Fig. 5(b) is a model diagram of a 10-pole 12-slot equivalent sinusoidal magnetic pole type motor.
Fig. 5(c) is a model diagram of a 10-pole 12-slot equivalent third harmonic injection type magnetic pole.
Fig. 6(a) is a no-load air gap flux density waveform diagram of three motors with different magnetic pole structures.
Fig. 6(b) is the no-load air gap flux density harmonic distribution diagram of three different magnetic pole structure motors.
Fig. 7 is a comparison graph of torque variation of three motors with different magnetic pole structures.
Fig. 8 is a graph comparing torque changes before and after third-order current harmonic injection.
Detailed Description
The technical scheme of the surface-mounted modulated magnetic pole structure design based on the specific resonance elimination method is firstly introduced below, and the technical scheme specifically comprises the following steps:
(1) determining modulated pole profile waveform function
The specific harmonic elimination technology is applied to the design process of the surface-mounted rotor magnetic pole to obtain a pair of under-pole modulated magnetic pole profile waveforms h0The Fourier series expansion expression is as follows:
wherein n (n ═ 1,3,5,7 …) represents the order of each harmonic; omega is angular velocity; t is time, cnAnd dnThe amplitudes of the sine and cosine components, respectively. As shown in figure 1, because the magnetic field generated by a pair of magnetic poles in a period 2 pi, the N pole faces upwards, and the S pole faces downwards, the two parts of the magnetic poles are in odd symmetry about a pi point. And when the modulation magnetic pole is designed, the magnetic pole of N pole (S pole) is divided into a plurality of blocks, so that the magnetic block under one pole is at [0, pi ]]The interval is symmetrical about pi/2. Therefore, even harmonics in the modulated pole profile waveform are eliminated, and cosine term harmonics are also eliminated. Further derivation of the modulated pole wheelThe expression of each harmonic amplitude in the profile waveform is as follows:
wherein h is the height of the magnetic pole, alphai(i is 1,2,3 … N) is the initial position angle of each magnetic pole in a quarter period, and should satisfy 0<α1<α2<α3…<αN<Pi/2, as shown in FIG. 1. The initial position angle of each magnetic pole is solved, the width and the relative position of each modulated magnetic pole under a pair of poles can be obtained according to the symmetry, and therefore the whole rotor magnetic pole structure is obtained. Let N number of alpha within a quarter periodiThe initial position angle, then (N-1) specific subharmonics can be eliminated.
(2) Determining equivalent sinusoidal modulation magnetic pole structure and position
Solving an equivalent sinusoidal magnetic pole structure of the motor, column-writing low-order harmonics which have large influence on the air gap flux density sine degree by utilizing an amplitude expression of each-order harmonic in a modulated magnetic pole profile waveform, and then setting amplitudes of other-order harmonics except a fundamental wave to be 0 to obtain a group of nonlinear equations consisting of the amplitude expressions of each-order harmonic:
and solving the nonlinear equation system to obtain the initial position angle of each modulation magnetic pole. Magnetic pole position angle alpha is obtained by utilizing impulse equality principleiAnd alpha is determined according to the aboveiAnd performing iterative solution by using the initial value as the initial value of the Matlab fslove solution function, wherein the basic iterative principle is a Newton iterative method, and when a program is converged, the approximate true solution of the nonlinear transcendental equation set can be obtained to obtain the magnetic pole structure and the distribution position, so that the rotor structure is further obtained.
(3) Determining the structure and the position of an equivalent third harmonic injection type modulation magnetic pole:
the low-order harmonic wave which has large influence on the air gap flux density sine degree is column-written by utilizing the amplitude expression of each-order harmonic wave in the modulated magnetic pole profile waveform, then the amplitudes of other-order harmonic waves except the fundamental wave and the third-order harmonic wave are set to be 0, the injection amount of the third-order harmonic wave is one sixth of the amplitude of the fundamental wave, and a group of nonlinear equations consisting of the amplitude expressions of each-order harmonic wave is obtained as follows:
solving a nonlinear equation set, and solving the initial position angle alpha of the magnetic pole by utilizing the impulse equality principleiAnd alpha is determined according to the aboveiAnd performing iterative solution by using the initial value as the initial value of the Matlab fslove solution function, wherein the basic iterative principle is a Newton iterative method, and when a program is converged, the approximate true solution of the nonlinear transcendental equation set can be obtained to obtain the magnetic pole structure and the distribution position, so that the whole rotor magnetic pole structure is obtained according to the symmetry.
(4) Establishing two equivalent rotor magnetic pole models and carrying out simulation verification
The surface-mounted double three-phase permanent magnet synchronous motor (sin type current) with a traditional magnetic pole structure and the motor (sin type current) with a novel equivalent sinusoidal magnetic pole structure are subjected to comparison finite element simulation, and the motor (sin type current) with equivalent third harmonic injected into a magnetic pole model and the motor (sin +3rd harmonic type current) with equivalent third harmonic injected into the magnetic pole model are subjected to verification of the correctness of theoretical analysis.
The following describes the embodiments of the present invention in detail based on the design of a 10p/12s motor, and the parameters of the designed motor are shown in table 1.
TABLE 1 parameters of a conventional dual three-phase surface-mounted motor
(1) And solving the amplitude expression of each harmonic in the modulated magnetic pole profile waveform. The specific harmonic elimination technology is applied to the magnetic pole design, and in order to simplify calculation in the actual design, a symmetrical arrangement mode is usually adopted. As shown in FIG. 1, aOpposite-pole lower modulation magnetic pole profile waveform h0The Fourier series expansion expression is as follows:
wherein:
wherein n (n ═ 1,3,5,7 …) represents the order of each harmonic; omega is angular velocity; t is time, cnAnd dnThe amplitudes of the sine and cosine components, respectively. As shown in figure 1, because the magnetic field generated by a pair of magnetic poles in a period 2 pi, the N pole faces upwards, and the S pole faces downwards, the two parts of the magnetic poles are in odd symmetry about a pi point. And when the modulation magnetic pole is designed, the magnetic pole of N pole (S pole) is divided into a plurality of blocks, so that the magnetic block under one pole is at [0, pi ]]The interval is symmetrical about pi/2. Thus:
h0(ωt)＝-h0(ωt+π) (4)
h0(ωt)＝h0(π-ωt) (5)
the compounds represented by the formulae (4) and (5) can be obtained by substituting the compounds represented by the formulae (2) and (3):
wherein h is the height of the magnetic pole, alphai(i is 1,2,3 … N) is the initial position angle of each magnetic pole in a quarter period, and should satisfy 0<α1<α2<α3…<αN<And pi/2. From equation (6), even harmonics in the modulated pole profile waveform are eliminated, and cosine harmonics are also eliminated. Thus, the amplitude of each harmonic in the modulated pole profile waveform can be obtainedThe values are expressed as:
the initial position angle alpha of each magnetic pole is solvediThe width and the relative position of each modulated magnetic pole under a pair of poles can be obtained according to the symmetry, and the whole rotor magnetic pole structure is obtained. Let N number of alpha within a quarter periodiThe initial position angle, then (N-1) specific subharmonics can be eliminated. In three-phase inverter symmetrical systems commonly used in certain harmonic elimination techniques, 3 and multiples thereof are not present and are therefore not considered. However, when applied to the design of the magnetic poles, the influence of harmonics 3 and multiples thereof needs to be considered in the magnetic field generated by the magnetic poles, so the harmonics which need to be eliminated are 3,5,7,9,11, …,2k-1(k is 2,3,4, …).
(2) And determining the equivalent sinusoidal magnetic pole structure and position of the motor. The invention takes a 12-slot 10-pole surface-mounted double three-phase permanent magnet motor as an example for design, and the distribution of air gap flux density harmonic waves generated by a traditional surface-mounted magnetic pole structure is shown in figure 2. As can be seen from FIG. 2, the higher amplitude 3,5,7,9 non-working subharmonics are the main factors affecting the sine degree of the air gap flux density. The number N of the position angles in the quarter period is selected to be 5, so that 3,5,7 and 9 times of 4 specific harmonics can be eliminated, and b is enabled to benDefining the modulation degree M as the amplitude b of the square wave fundamental wave for the amplitude of the n-th harmonic wave1Amplitude h of square wavemThe ratio of (a) to (b), namely:
taking the modulation degree as M to be 1, and the nonlinear equation formed by the corresponding amplitude expressions of each harmonic as follows:
therefore, the initial position angle of each magnetic pole can be obtained by only solving the solution of the equation set, and then the rotor is obtainedThe magnetic pole structure can eliminate specific subharmonic in air gap flux density. However, this nonlinear transcendental system of equations cannot be solved directly, and alpha needs to be calculatediAnd solving the initial value by using an iterative method.
The solution of the nonlinear equation set is to obtain the core of the rotor structure of the modulated magnetic pole, the initial value is selected by adopting the impulse equality principle, as shown in fig. 3, P square magnetic poles are arranged in a half period, the centers of all the magnetic poles are equidistant, the interval is pi/P, the amplitudes are all hmTherefore, the center line position angle of the ith magnetic pole is:
the height of the sine waveform corresponding to the center position of the ith magnetic pole is as follows:
h1i＝b1sinθi (11)
width W of ith magnetic poleiCan be calculated as:
thus, the starting and ending position angles of the ith block of magnetic poles are:
taking P as 5, calculating an initial value of the obtained magnetic pole position angle as follows:
TABLE 2 initial values of magnetic pole position angle
MatlabThe method has efficient numerical calculation and symbol calculation functions, comprises a large number of calculation algorithms, can directly solve a large-scale nonlinear transcendental equation set by a Matlab fslove function contained in a tool box, and has a Newton iteration principle, so that the alpha is calculated according to the principleiAnd performing iterative solution by using the initial value as the initial value of the fslove function, and obtaining an approximate true solution of the nonlinear transcendental equation set when the program is converged. The magnetic pole position angle parameters obtained by actual solution are shown in table 3, and the widths and positions corresponding to 5 magnetic poles can be obtained according to the symmetry of the modulated magnetic pole under one pole relative to pi/2, and then the whole rotor magnetic pole structure can be obtained according to the symmetry.
TABLE 3 actual pole position Angle parameters
(3) And determining the structure and position of the equivalent third harmonic injection type magnetic pole of the motor. It is known that, when the rotor magnetic pole of the surface-mount motor is cut into a sinusoidal structure, torque ripple is reduced, but torque density is also greatly reduced. Therefore, in order to increase the torque without aggravating the torque fluctuation, a scheme of injecting third harmonic in the shape of the sinusoidal magnetic pole is proposed, namely, the fundamental air gap flux density amplitude can be increased by injecting 3 harmonic under the condition of ensuring that the maximum thickness of the magnetic pole is not changed. Besides, under the condition that two sets of windings of the double three-phase motor are shifted by 30 degrees in phase, third harmonic current can be injected into the stator side to interact with third harmonic in air gap flux density to generate electromagnetic torque, and the torque density is further improved. In the equivalent triple-harmonic injection type magnetic pole structure, in order to ensure that the maximum thicknesses of the magnetic poles before and after injection are the same and the maximum torque is obtained at the same time, the amplitude of the triple harmonic of the injection magnetic pole is 1/6 of the amplitude of the fundamental wave, at the moment, the function of the shape of the magnetic pole is as shown in formula (15), and the shape of the magnetic pole after injection of the triple harmonic is as shown in fig. 4.
As can be seen from fig. 4, the magnetic pole shape function only includes fundamental waves and third harmonics, and the nonlinear equation set formed by the corresponding amplitude expressions of the harmonics is:
the position angle parameter of the equivalent third harmonic injection type magnetic pole obtained by solving the position angle parameter by using the Matlab fslove function is shown in table 4.
TABLE 4 triple harmonic injection pole position angle parameters
According to the symmetry of modulation magnetic poles under one pole about pi/2, the width and position corresponding to 5 magnetic poles can be obtained, and further, the whole rotor magnetic pole structure can be obtained according to the symmetry.
(4) And establishing two equivalent rotor magnetic pole models and carrying out simulation verification. A finite element simulation model of the finally designed double three-phase permanent magnet synchronous motor with the equivalent sinusoidal magnetic pole structure and the equivalent third harmonic injection magnetic pole structure and the traditional surface-mounted magnetic pole structure motor is obtained on the basis of the steps (2) and (3) and is shown in fig. 5. The motor no-load air gap flux density waveform adopting three different magnetic pole structures is obtained through simulation, and is shown in fig. 6 (a). The no-load air gap flux density harmonic distribution diagram obtained by Fourier decomposition is shown in fig. 6(b), and compared with the traditional monoblock permanent magnet structure, 3,5,7 and 9 times of harmonics in the air gap flux density generated by the equivalent sinusoidal magnetic pole of the specific resonance elimination technology are almost completely eliminated, the sine degree of the air gap flux density waveform is remarkably improved, and therefore the effectiveness of the specific resonance elimination technology is verified. But the content of the fundamental wave (0.79) is obviously reduced compared with the traditional monoblock magnetic pole structure (0.98), so the average torque of the motor is also reduced. From the view of the air gap flux density generated by the equivalent triple harmonic injection type magnetic pole, compared with each subharmonic of the air gap flux density corresponding to the equivalent sinusoidal magnetic pole, except the triple harmonic, the rest subharmonics are not increased, and simultaneously, the fundamental flux density (0.9) is greatly improved compared with the equivalent sinusoidal magnetic pole, so that the equivalent triple harmonic injection type magnetic pole realized by adopting a specific resonance elimination technology can increase the torque density of the motor, and further, the effectiveness of the specific resonance elimination technology is explained. The average torque distribution of the three motors at sinusoidal current is shown in fig. 7. The average torque pair generated by a double three-phase permanent magnet synchronous motor with an equivalent triple-harmonic injection magnetic pole structure under the condition that the sine current and the triple-harmonic injection current have the same amplitude is shown in fig. 8. Finally, the electromagnetic performance parameters of the four motors are arranged, and are shown in the following table:
TABLE 5 comparison of dual three-phase PMSM Performance
The result shows that the novel magnetic pole structure design method realizes the improvement of the sine degree of the air gap flux density waveform, effectively reduces the content of the non-working subharmonic in the air gap flux density, and effectively reduces the torque fluctuation of the motor. Meanwhile, the novel magnetic pole structure design method also realizes the 3-order harmonic injection of the air gap magnetic field, improves the torque density of the motor on the basis of not deteriorating the torque fluctuation of the motor, further utilizes the interaction of the third harmonic current and the 3-order harmonic of the air gap magnetic density to generate extra forward torque, and superposes the extra forward torque with the torque generated by the air gap fundamental component, further improves the torque density of the motor, and improves the performance of the double three-phase permanent magnet synchronous motor.
Claims (10)
1. A surface-mounted modulation magnetic pole structure design method based on a specific harmonic elimination method comprises the following steps:
(1) deducing a magnetic pole specific harmonic elimination principle to obtain an amplitude expression of each harmonic in a modulated magnetic pole profile waveform;
(2) designing and solving an equivalent sinusoidal magnetic pole structure of the motor according to the amplitude expression of each subharmonic;
(3) designing and solving an equivalent third harmonic injection type magnetic pole structure of the motor according to the amplitude expression of each subharmonic;
(4) simulation verification: carrying out simulation verification on the double three-phase permanent magnet synchronous motor provided with the equivalent sinusoidal magnetic pole model designed and solved in the step (2) and the equivalent third harmonic injection magnetic pole model designed and solved in the step (3), wherein in addition to the sine current, the third harmonic current is injected into the winding, so that the third harmonic current interacts with the third harmonic in the air gap flux density to improve the electromagnetic torque; and carrying out finite element simulation and verification with the traditional surface-mounted magnetic pole structure motor.
2. The design method according to claim 1, wherein the method of step (1) is as follows:
1) applying Specific Harmonic Elimination Technology (SHET) to the design process of the surface-mounted rotor magnetic pole to obtain a pair of under-pole modulated magnetic pole profile waveforms h0The Fourier series expansion expression of (1);
2) because the magnetic fields generated by a pair of magnetic poles in a period of 2 pi are in odd symmetry with the pi point, and when the modulation magnetic poles are designed, the magnetic poles of the N pole and the S pole are respectively divided into a plurality of blocks, so that the magnetic blocks under one pole are in symmetry with pi/2 in the interval of [0, pi ], even harmonics in the profile waveform of the modulation magnetic poles can be eliminated, cosine term harmonics can be eliminated, and further, the amplitude expression of each harmonic in the profile waveform of the modulation magnetic poles is obtained.
3. The design method according to claim 1, wherein the amplitude expression of each harmonic in the modulated pole profile waveform obtained in step (1) is as follows:
wherein n (n ═ 1,3,5,7 …) represents the order of each harmonic; omega is angular velocity; t is time, h is pole height, alphai(i is 1,2,3 … N) is the initial position angle of each magnetic pole in a quarter period, and should satisfy 0<α1<α2<α3…<αN<Pi/2, the initial position angle of each magnetic pole is solved, and a pair of poles can be obtained according to symmetryModulating the width and the relative position of each lower block of magnetic pole so as to obtain the whole rotor magnetic pole structure; let N number of alpha within a quarter periodiInitial position angle, eliminating (N-1) specific subharmonics.
4. The design method according to claim 1, wherein the method in step (2) is as follows:
1) solving the equivalent sinusoidal magnetic pole structure of the motor: the method comprises the steps that low-order harmonics which have large influence on air gap flux density sine degree are written in a column mode by using amplitude expressions of each-order harmonic in modulated magnetic pole profile waveforms, then amplitudes of other-order harmonics except fundamental waves are set to be 0, and a first nonlinear equation set consisting of the amplitude expressions of each-order harmonic is obtained;
2) solving the first nonlinear equation system to obtain the position angle of each magnetic pole: magnetic pole position angle alpha is obtained by utilizing impulse equality principleiAnd according to the calculated alphaiAnd (4) carrying out iterative solution on the initial value, and obtaining an approximate true solution of the nonlinear transcendental equation set when the program is converged to obtain the magnetic pole structure and the distribution position so as to further obtain the rotor structure.
5. The design method of claim 4, wherein iteratively solving the first set of non-linear equations uses a newton iteration method.
6. A design method according to claim 5, wherein the first system of non-linear equations is solved according to the solved αiAnd performing iterative solution by using the initial value as the initial value of the Matlab fslove solution function.
7. The design method according to claim 1, wherein the method in step (3) is as follows:
1) solving an equivalent third harmonic injection type magnetic pole structure: the low-order harmonic with large influence on the air gap flux density sine degree is written in a column mode by using the amplitude expression of each-order harmonic in the modulated magnetic pole profile waveform, then the amplitudes of other-order harmonics except the fundamental wave and the third harmonic are set to be 0, and a second nonlinear equation set consisting of the amplitude expressions of each-order harmonic is obtained;
2) solving the second nonlinear equation system to obtain the position angle of each magnetic pole: magnetic pole position angle alpha is obtained by utilizing impulse equality principleiAnd according to the calculated alphaiAnd carrying out iterative solution on the initial value, and obtaining an approximate true solution of the nonlinear transcendental equation set when the program is converged to obtain the magnetic pole structure and the distribution position, thereby obtaining the whole rotor magnetic pole structure according to the symmetry.
8. The design method of claim 7, wherein the second system of non-linear equations is iteratively solved using newton's iteration.
9. The design method of claim 8, wherein the second system of non-linear equations is solved based on the solved αiAnd performing iterative solution by using the initial value as the initial value of the Matlab fslove solution function.
10. The design method according to claim 1, wherein in step (4), in order to ensure that the current amplitudes before and after the harmonic injection are the same, so as to achieve that the current peak value does not exceed the current limit value of the inverter power supply, the optimal value of the current amplitude of the injected third harmonic is 1/6 of the fundamental wave amplitude.
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