CN114142640B - Surface-mounted modulation magnetic pole structure design method based on specific resonance elimination method - Google Patents
Surface-mounted modulation magnetic pole structure design method based on specific resonance 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 resonance elimination method, which comprises the following steps: deriving a magnetic pole specific harmonic elimination principle to obtain an amplitude expression of each subharmonic in the 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; according to the amplitude expression of each subharmonic, designing and solving an equivalent third harmonic injection type magnetic pole structure of the motor; simulation verification: and (3) performing 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 machining the special-shaped outer contour of the harmonic 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 the simple structure and small magnetic leakage. At present, the performance requirements of various industrial application fields on the 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 key point and a difficulty in the current motor design field. The performances of electromagnetic torque, torque fluctuation, vibration noise and the like of the permanent magnet motor are closely related to the size of air gap flux density and waveform sine, the rotor magnetic poles of the traditional surface-mounted permanent magnet motor are generally formed by arranging whole magnetic poles according to a specified pole arc coefficient, the generated air gap magnetic field has poor sine degree and contains various non-working subharmonics, 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 loss of the motor.
In recent years, scholars at home and abroad have made a great deal of researches on the magnetic pole structure optimization design of the surface-mounted permanent magnet motor, and scholars propose a method for combining the equal-width segmented magnetic poles and the magnetic pole materials with different magnetization intensities, so that the air gap magnetic density waveform sine degree is improved, but the magnetic pole performance difference among different materials is large, and the processing and manufacturing difficulty is increased; for the method of carrying out eccentric pole cutting on the outer pole arc of the rotor magnetic pole, a simple model is utilized to deduce the 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; for the method that the pole cutting is of the sine-shaped 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 degree of the waveform of the air gap flux density of the motor can be higher by utilizing the sine-shaped magnetic pole structure, the torque fluctuation of the motor is effectively reduced, and the special arc shape of the outline of the motor brings great difficulty to the production and processing of the magnetic pole.
The specific harmonic elimination modulation method is proposed by Patel H.S. and Hoft R.G. and the like in 1973, and is mainly applied to the field of variable frequency power supplies. When the three-level inverter is applied to the driving occasion of a high-power motor, in order to reduce the switching frequency of a power device and thus reduce the switching loss, a specific harmonic cancellation technology (SHET) is needed to cancel low-order harmonics existing in the output voltage waveform, so that the current pulsation is reduced, and the performance of the 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 the output phase voltage of the three-phase inverter is utilized, the amplitude of the specific subharmonic to be eliminated is set to be zero as constraint, a nonlinear overrunning equation set taking a switch angle alpha as an unknown number is further solved, and the specific harmonic in the output voltage of the inverter is eliminated finally through modulation [3] 。
Reference is made to:
[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, hasmukh, S, et al Generalized Techniques of Harmonic Elimination and Voltage Control in Thyristor Inverters, part II- - -Voltage Control Techniques [ J ]. Industry Applications, IEEE Transactions on,1974.
[3] Wei Yuanzhi analysis and control of residual harmonics in specific detuning techniques [ D ]. Harbine engineering university, 2019.
Disclosure of Invention
The invention provides a novel surface-mounted modulation magnetic pole structure design method, which is based on a specific harmonic elimination technical principle, utilizes a Fourier series model of a modulation magnetic pole profile waveform, takes the amplitude of a specific subharmonic to be eliminated or injected as constraint, solves a nonlinear overrunning equation taking the initial position angle of the modulation magnetic pole as an unknown number, obtains the initial position angle of the modulation magnetic pole, and further obtains the rotor structure of the whole modulation magnetic pole by utilizing symmetry, thereby realizing elimination and injection of the specific harmonic of an air gap magnetic field of a motor, effectively improving the performance of a surface-mounted double-three-phase permanent magnet synchronous motor, and reducing the difficulty of processing the special-shaped outer profile of the harmonic pole structure. The technical scheme is as follows:
a surface-mounted modulation magnetic pole structure design method based on a specific resonance elimination method comprises the following steps:
(1) Deriving a magnetic pole specific harmonic elimination principle to obtain an amplitude expression of each subharmonic in the 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) According to the amplitude expression of each subharmonic, designing and solving an equivalent third harmonic injection type magnetic pole structure of the motor;
(4) Simulation verification: simulation verification is carried out 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), and under the condition that the third harmonic current is injected into the winding in addition to the sinusoidal current, the winding interacts with the third harmonic in the air gap flux density to promote electromagnetic torque; and carrying out finite element simulation and verification on the motor with the traditional surface-mounted magnetic pole structure.
The method of step (1) may be as follows:
1) Applying specific harmonic cancellation technique (SHET) to the design process of the surface-mounted rotor pole to obtain a pair of modulated pole profile waveforms h 0 Fourier series expanded expressions of (a);
2) Because the magnetic field generated by a pair of magnetic poles in a period 2 pi is odd-symmetrical about pi point, and when the modulated magnetic poles are designed, the magnetic poles of N pole and S pole are respectively divided into a plurality of blocks, so that the magnetic blocks under one pole are symmetrical about pi/2 in the [0, pi ] interval, even harmonic waves in the profile waveform of the modulated magnetic poles can be eliminated, cosine harmonic waves are eliminated, and the amplitude expression of each subharmonic wave in the profile waveform of the modulated magnetic poles is further obtained.
The amplitude expression of each subharmonic in the modulated magnetic pole profile waveform obtained in the step (1) is as follows:
wherein n (n=1, 3,5,7, …) is the order of each subharmonic; omega is the angular velocity; t is time, h is magnetic pole height, alpha i (i=1, 2,3 … N) is the initial position angle of each block magnetic pole in the quarter period, and 0 should be satisfied<α 1 <α 2 <α 3 …<α N <Pi/2, solving the initial position angle of each magnetic pole, and solving the width and the relative position of each modulation magnetic pole under a pair of poles according to symmetry, thereby obtaining the whole rotor magnetic pole structure; let N alpha in quarter cycle i The initial position angle, eliminating (N-1) specific subharmonics.
The method in step (2) may be as follows:
1) Solving an equivalent sinusoidal magnetic pole structure of the motor: using each subharmonic amplitude expression in the modulated magnetic pole profile waveform, writing low subharmonic with great influence on the air gap flux density sine degree, and setting the subharmonic amplitudes except the fundamental wave to 0 to obtain a group of first nonlinear equation set consisting of each subharmonic amplitude expression;
2) Solving a first nonlinear equation set to obtain the position angle of each magnetic pole: determining the magnetic pole position angle alpha based on impulse equality principle i And based on the initial value of alpha i And (3) performing iterative solution on the initial value, and obtaining an approximate true solution of a nonlinear overrunning equation set when the program converges to obtain a magnetic pole structure and distribution positions and further obtain a rotor structure.
The iterative solution of the first nonlinear equation set can adopt Newton iteration method and can be based on the obtained alpha i And the initial value is used as the initial value of the Matlab fslove solving function to carry out iterative solving.
The method in step (3) may be as follows:
1) Solving an equivalent third harmonic injection type magnetic pole structure: using the amplitude expressions of each subharmonic in the modulated magnetic pole profile waveform, writing low subharmonic with great influence on the air gap flux density sine degree, and setting the amplitude of other subharmonic except the fundamental wave and the third harmonic to 0 to obtain a group of second nonlinear equation set consisting of the amplitude expressions of each subharmonic;
2) Solving a second nonlinear equation set to obtain the position angle of each magnetic pole: determining the magnetic pole position angle alpha based on impulse equality principle i And based on the initial value of alpha i The initial value is used as the initial value of the Matlab fslove solving function to carry out iterative solution, the basic iterative principle is Newton iterative method, and when the program converges, the approximate true solution of the nonlinear overrunning equation set can be obtained, and the magnetic pole structure and the distribution position are obtained, so that the whole rotor magnetic pole structure is obtained according to symmetry.
Carrying out iterative solution on the second nonlinear equation set, and adopting a Newton iteration method; can be based on the alpha i And the initial value is used as the initial value of the Matlab fslove solving function to carry out iterative solving.
In the step (4), in order to ensure that the current amplitude values 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 value of the third harmonic injection is 1/6 of the fundamental wave amplitude value.
The invention provides a novel surface-mounted modulation magnetic pole structure design method based on a specific harmonic elimination technical principle, and provides a calculation method for the number, the size and the position of modulation magnetic poles. The method aims to solve the width and the position angle of the magnetic pole by utilizing a specific harmonic elimination technology, and realize elimination and injection of specific harmonic of an empty air gap field of the motor. The finite element analysis results show that the novel magnetic pole structure design method provided by the invention realizes the improvement of the waveform sine degree of the air gap flux density, effectively reduces the non-working subharmonic content 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 injection of 3rd harmonic waves of the air gap field, further improves the torque density of the motor on the basis of not deteriorating the torque fluctuation of the motor, and provides a thought for designing a permanent magnet synchronous motor with high torque density and low torque fluctuation.
Drawings
Fig. 1 is a theoretical waveform diagram of a modulated pole and a sinusoidal pole.
FIG. 2 is a graph of the harmonic distribution of the empty air gap flux density of a conventional 10-pole 12-slot motor.
Fig. 3 is a theoretical waveform diagram of a modulated pole and a sinusoidal pole.
Fig. 4 is a theoretical waveform diagram of a modulated pole and a 3rd harmonic injection pole.
Fig. 5 (a) is a diagram of a conventional 10-pole 12-slot surface-mounted magnetic pole structure motor.
Fig. 5 (b) is a model diagram of a 10-pole 12-slot equivalent sinusoidal magnetic pole motor.
Fig. 5 (c) is a motor model diagram of a 10-pole 12-slot equivalent third harmonic injection type magnetic pole.
Fig. 6 (a) is a waveform diagram of an empty air gap magnetic seal of a three-pole structure motor.
Fig. 6 (b) shows the harmonic distribution diagram of the empty air gap flux density of three motors with different magnetic pole structures.
Fig. 7 is a graph comparing torque changes of three motors with different magnetic pole structures.
Fig. 8 is a graph of torque variation versus time before and after injection of the third harmonic current.
Detailed Description
The technical scheme of the surface-mounted modulation magnetic pole structure design based on the specific resonance elimination method is firstly introduced, and specifically comprises the following steps:
(1) Determining modulated pole profile waveform functions
Applying specific harmonic elimination technology to design process of surface-mounted rotor magnetic pole to obtain a pair of modulated magnetic pole profile waveforms h 0 The fourier series expansion expression of (a) is:
wherein n (n=1, 3,5,7, …) is the order of each subharmonic; omega is the angular velocity; t is time, c n And d n The amplitudes of the sine component and the cosine component, respectively. As shown in fig. 1, since the magnetic field generated by a pair of magnetic poles is in a period of 2pi, the N pole is upward and the S pole is downward, the two magnetic poles are in odd symmetry about pi point. And when the modulated magnetic pole is designed, the magnetic pole of N pole (S pole) is divided into several blocks, so that the magnetic block under one pole is 0, pi]The interval is again symmetrical about pi/2. Even harmonics in the modulated pole profile waveform can be eliminated and cosine term harmonics can be eliminated. The amplitude expression of each subharmonic in the modulated magnetic pole profile waveform can be further deduced as follows:
wherein h is the height of the magnetic pole, alpha i (i=1, 2,3 … N) is the initial position angle of each block magnetic pole in the quarter period, and 0 should be satisfied<α 1 <α 2 <α 3 …<α N <Pi/2, as shown in FIG. 1. The initial position angle of each magnetic pole is solved, and the width and the relative position of each modulation magnetic pole under a pair of poles can be solved according to symmetry, so that the whole rotor magnetic pole structure is obtained. Let N alpha in quarter cycle i The angle of the initial position of the device,then (N-1) specific subharmonics can be eliminated.
(2) Determining equivalent sinusoidal modulation pole structure and position
Solving an equivalent sinusoidal magnetic pole structure of the motor, utilizing each subharmonic amplitude expression in a modulated magnetic pole profile waveform, writing low subharmonic with great influence on the air gap flux density sine degree, and setting the subharmonic amplitude except for a fundamental wave to be 0 to obtain a nonlinear equation set consisting of each subharmonic amplitude expression:
and solving a nonlinear equation set to obtain the initial position angle of each modulating magnetic pole. Determining the magnetic pole position angle alpha based on impulse equality principle i And according to the above alpha i The initial value is used as the initial value of the Matlab fslove solving function to carry out iterative solution, the basic iterative principle is Newton iterative method, and when the program converges, the approximate true solution of the nonlinear overrunning equation set can be obtained, the magnetic pole structure and the distribution position are obtained, and the rotor structure is further obtained.
(3) Determining the structure and the position of an equivalent third harmonic injection type modulation magnetic pole:
by using the expressions of the amplitude of each subharmonic in the modulated magnetic pole profile waveform, the low subharmonic with larger influence on the air gap flux density sine degree is written, then the amplitudes of other subharmonics except the fundamental wave and the third harmonic are set to be 0, the injection quantity of the third harmonic is one sixth of the amplitude of the fundamental wave, and a group of nonlinear equations consisting of the expressions of the amplitude of each subharmonic is obtained:
solving a nonlinear equation system, and solving an initial position angle alpha of the magnetic pole by utilizing impulse equality principle i And according to the above alpha i The initial value is used as the initial value of Matlab fslove solving function to carry out iterative solution, and the basic iterative principle is thatAnd when the program converges, the Newton iteration method can obtain the approximate true solution of the nonlinear overrunning equation set to obtain the magnetic pole structure and the distribution position, thereby obtaining the whole rotor magnetic pole structure according to symmetry.
(4) Establishing two equivalent rotor magnetic pole models and performing simulation verification
The surface-mounted double-three-phase permanent magnet synchronous motor (sin-type current) with the traditional magnetic pole structure, the motor (sin-type current) with the novel equivalent sinusoidal magnetic pole structure, the motor (sin-type current) with the equivalent third harmonic injection magnetic pole model and the motor (sin+3rd harmonic type current) with the equivalent third harmonic injection magnetic pole model are subjected to contrast finite element simulation, and the correctness of theoretical analysis is verified.
The following describes embodiments of the present invention in detail based on a 10p/12s motor, and parameters of the designed motor are shown in Table 1.
Table 1 parameters of conventional double three-phase surface-mounted motor
(1) And solving the amplitude expression of each subharmonic in the modulated magnetic pole profile waveform. Specific harmonic cancellation techniques are applied to pole designs, which are typically symmetrically arranged for simplicity of computation. As shown in fig. 1, a pair of modulated pole profile waveforms h 0 The fourier series expansion expression of (a) is:
wherein:
wherein n (n=1, 3,5,7, …) is the order of each subharmonic; omega is the angular velocity; t is time, c n And d n The amplitudes of the sine component and the cosine component, respectively. As shown in fig. 1, since the magnetic field generated by a pair of magnetic poles is in a period of 2pi, the N pole is upward and the S pole is downward, the two magnetic poles are in odd symmetry about pi point. And when the modulated magnetic pole is designed, the magnetic pole of N pole (S pole) is divided into several blocks, so that the magnetic block under one pole is 0, pi]The interval is again symmetrical about pi/2. Thus:
h 0 (ωt)＝-h 0 (ωt+π) (4)
h 0 (ωt)＝h 0 (π-ωt) (5)
the substitution of the formulas (4) and (5) into the formulas (2) and (3) respectively can be obtained:
wherein h is the height of the magnetic pole, alpha i (i=1, 2,3 … N) is the initial position angle of each block magnetic pole in the quarter period, and 0 should be satisfied<α 1 <α 2 <α 3 …<α N <Pi/2. As can be seen from equation (6), even harmonics are eliminated from the modulated pole profile waveform, and cosine harmonics are eliminated. Thus, the amplitude of each subharmonic in the modulated pole profile waveform is expressed as:
solving the initial position angle alpha of each magnetic pole i The width and the relative position of each modulation magnetic pole under a pair of poles can be obtained according to the symmetry, so that the whole rotor magnetic pole structure is obtained. Let N alpha in quarter cycle i The initial position angle can eliminate (N-1) specific subharmonics. In a symmetrical system of a three-phase inverter commonly used in a specific harmonic elimination technology, 3 and multiples thereof are not existed, so that the symmetrical system is not considered. However, when the method is applied to the design of magnetic poles, the magnetic field generated by the magnetic poles needs to be considered to be 3 times and multiples thereofThe harmonics are affected, so the harmonics that it is desired to cancel are 3,5,7,9,11, …,2k-1 (k=2, 3,4, …).
(2) And determining the equivalent sinusoidal magnetic pole structure and the equivalent sinusoidal magnetic pole 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 generated by a traditional surface-mounted magnetic pole structure is shown in figure 2. As can be seen from fig. 2, the higher magnitude of the 3,5,7, and 9 non-operating subharmonics are the primary factors affecting the air gap flux density sinusoid. Selecting the number of position angles in a quarter period, N=5, so that 3,5,7 and 9 times of 4 specific harmonic waves can be eliminated to enable b to be n For the amplitude of the n-order harmonic, a modulation degree M is defined as a square wave fundamental wave amplitude b 1 And square wave amplitude h m Ratio of (2), namely:
taking a nonlinear equation set consisting of the corresponding subharmonic amplitude expressions with a modulation degree of M=1 as follows:
therefore, the initial position angle of each magnetic pole can be obtained by solving the solution of the equation set, so that the magnetic pole structure of the rotor is obtained, and the aim of eliminating specific subharmonic in the air gap flux density is fulfilled. However, the nonlinear transcendental equation system cannot be directly solved and alpha is calculated i And (5) initial value and solving by using an iteration method.
The nonlinear equation system is solved by obtaining the core of the modulated magnetic pole rotor structure, the initial value is selected by adopting the impulse equality principle, as shown in figure 3, P square magnetic poles are arranged in a half period, the centers of the magnetic poles are equidistant, the distance is pi/P, and the amplitude is h m The centerline position angle of the i-th block pole is therefore:
the height of the sine waveform corresponding to the center position of the ith block magnetic pole is as follows:
h 1i ＝b 1 sinθ i (11)
width W of ith block pole i It can be calculated as:
thus, the start and end position angles of the ith block pole are:
taking p=5, the initial value of the available magnetic pole position angle is calculated as follows:
TABLE 2 initial parameters of magnetic pole position angle
Matlab has high-efficiency numerical calculation and symbol calculation functions, comprises a large amount of calculation algorithms, the Matlab fslove function contained in a toolbox can directly solve a large nonlinear overrun equation set, and the basic iteration principle is Newton iteration method, so that alpha is solved according to the above i And (4) performing iterative solution by taking the initial value as the initial value of the fslove function, and obtaining the approximate true solution of the nonlinear overrun equation set when the program converges. The parameters of the position angles of the magnetic poles obtained by actual solving are shown in table 3, and according to the symmetry of the modulation magnetic pole under one pole about pi/2, the width and the position corresponding to 5 magnetic poles can be obtained respectively, and then the magnetic pole structure of the whole rotor can be obtained according to the symmetry.
TABLE 3 actual magnetic pole position angle parameters
(3) And determining the structure and the position of the equivalent third harmonic injection type magnetic pole of the motor. It is known that when the pole segments of the rotor of a surface mount motor are of a sinusoidal configuration, torque ripple is reduced, but torque density is also greatly reduced. Therefore, in order to increase the torque without aggravating the torque ripple, a scheme of injecting the third harmonic into the sinusoidal magnetic pole shape is proposed, that is, the fundamental air gap density amplitude can be increased by injecting the 3rd harmonic while ensuring the maximum thickness of the magnetic pole is unchanged. Moreover, under the condition that the phase of two sets of windings of the double three-phase motor is shifted by 30 degrees, the electromagnetic torque can be generated by injecting third harmonic current on the stator side to enable the third harmonic current to interact with third harmonic in the air gap flux density, and the torque density is further improved. In the equivalent third harmonic injection type magnetic pole structure, in order to ensure that the maximum thickness of the magnetic poles before and after injection is the same, and meanwhile, the maximum torque is obtained, the third harmonic amplitude of the injection magnetic pole is 1/6 of the fundamental amplitude, at this time, the magnetic pole shape function is shown as a formula (15), and the magnetic pole shape after the injection of the third harmonic is shown as a figure 4.
As can be seen from fig. 4, the magnetic pole shape function only contains fundamental wave and third harmonic, and the nonlinear equation set composed of the corresponding subharmonic amplitude expressions is:
and solving the magnetic pole by using a Matlab fslove function, wherein the position angle parameters of the equivalent third harmonic injection type magnetic pole obtained by actual solving are shown in a table 4.
TABLE 4 third harmonic injection pole position angle parameters
According to the symmetry of modulation magnetic pole under one pole about pi/2, the width and position corresponding to 5 magnetic poles can be obtained, and then the whole rotor magnetic pole structure can be obtained according to the symmetry.
(4) And establishing two equivalent rotor magnetic pole models and performing simulation verification. And (3) obtaining a final design of a double three-phase permanent magnet synchronous motor with an equivalent sinusoidal magnetic pole structure and an equivalent third harmonic injection magnetic pole structure and a finite element simulation model of a traditional surface-mounted magnetic pole structure motor on the basis of the steps (2) and (3), wherein the finite element simulation model is shown in figure 5. The motor no-load air gap flux density waveforms adopting three different magnetic pole structures are obtained through simulation, as shown in fig. 6 (a). As shown in FIG. 6 (b), compared with the conventional whole permanent magnet structure, the harmonic distribution diagram of the empty air gap flux density obtained by Fourier decomposition is that 3,5,7 and 9 harmonics are almost completely eliminated in the air gap flux density generated by the equivalent sinusoidal magnetic poles by using a specific harmonic elimination technology, and the waveform sine degree of the air gap flux density is obviously improved, so that the effectiveness of the specific harmonic elimination technology is verified. But the fundamental wave (0.79) content is obviously reduced compared with the traditional integral magnetic pole structure (0.98), so that the average torque of the motor is also reduced. Compared with each subharmonic of the air gap flux density corresponding to the equivalent sinusoidal magnetic pole, the subharmonic except the third harmonic is not increased from the air gap flux density generated by the equivalent third harmonic injection magnetic pole, and meanwhile, the fundamental flux density (0.9) is also greatly improved compared with the equivalent sinusoidal magnetic pole, so that the torque density of the motor can be increased by adopting the equivalent third harmonic injection magnetic pole realized by adopting a specific harmonic elimination technology, and the effectiveness of the specific harmonic elimination technology is further illustrated. 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 equipped with an equivalent third harmonic injection magnetic pole structure under the condition of the same amplitude of sinusoidal current and third harmonic injection current is as shown in fig. 8. Finally, the electromagnetic performance parameters of the four motors are sorted, and the following table shows:
table 5 comparison of performance of double three-phase permanent magnet synchronous motor
The result shows that the novel magnetic pole structure design method realizes the improvement of the waveform sine degree of the air gap flux density, effectively reduces the non-working subharmonic content 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 injection of the 3rd harmonic 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 3rd harmonic of the air gap magnetic field to generate additional forward torque, and is overlapped with the torque generated by the air gap fundamental wave component, so that the torque density of the motor is further improved, and the performance of the double three-phase permanent magnet synchronous motor is improved.
Claims (6)
1. A surface-mounted modulation magnetic pole structure design method based on a specific resonance elimination method comprises the following steps:
(1) Deriving a magnetic pole specific harmonic elimination principle to obtain an amplitude expression of each subharmonic in the modulated magnetic pole profile waveform, wherein the method comprises the following steps:
1) Applying specific harmonic cancellation technique (SHET) to the design process of the surface-mounted rotor pole to obtain a pair of modulated pole profile waveforms h 0 Fourier series expanded expressions of (a);
2) Because the magnetic field generated by a pair of magnetic poles in a period 2 pi is odd-symmetrical about pi point, and when the modulated 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 symmetrical about pi/2 in a [0, pi ] interval, even harmonic waves in the profile waveform of the modulated magnetic poles can be eliminated, cosine harmonic waves are also eliminated, amplitude expressions of all subharmonic waves in the profile waveform of the modulated magnetic poles are further obtained, and the amplitude expressions of all subharmonic waves in the profile waveform of the modulated magnetic poles are obtained as follows:
wherein n (n=1, 3,5,7, …) is the order of each subharmonic; omega is angular velocityA degree; t is time, h is magnetic pole height, alpha i (i=1, 2,3 … N) is the initial position angle of each block magnetic pole in the quarter period, and 0 should be satisfied<α 1 <α 2 <α 3 …<α N <Pi/2, solving the initial position angle of each magnetic pole, and solving the width and the relative position of each modulation magnetic pole under a pair of poles according to symmetry to obtain the whole rotor magnetic pole structure; let N alpha in quarter cycle i Initial position angle, eliminating (N-1) specific subharmonics;
(2) According to the expression of the amplitude of each subharmonic, designing and solving the equivalent sinusoidal magnetic pole structure of the motor, and the method comprises the following steps:
1) Solving an equivalent sinusoidal magnetic pole structure of the motor: using each subharmonic amplitude expression in the modulated magnetic pole profile waveform, writing low subharmonic with great influence on the air gap flux density sine degree, and setting the subharmonic amplitudes except the fundamental wave to 0 to obtain a group of first nonlinear equation set consisting of each subharmonic amplitude expression;
2) Solving a first nonlinear equation set to obtain the position angle of each magnetic pole: determining the magnetic pole position angle alpha based on impulse equality principle i And based on the initial value of alpha i Performing iterative solution on the initial value, and obtaining an approximate true solution of a nonlinear overrunning equation set when the program converges to obtain a magnetic pole structure and distribution positions and further obtain a rotor structure;
(3) According to the expression of the amplitude of each subharmonic, the method for designing and solving the equivalent third harmonic injection type magnetic pole structure of the motor is as follows:
1) Solving an equivalent third harmonic injection type magnetic pole structure: using the amplitude expressions of each subharmonic in the modulated magnetic pole profile waveform, writing low subharmonic with great influence on the air gap flux density sine degree, and setting the amplitude of other subharmonic except the fundamental wave and the third harmonic to 0 to obtain a group of second nonlinear equation set consisting of the amplitude expressions of each subharmonic;
2) Solving a second nonlinear equation set to obtain the position angle of each magnetic pole: determining the magnetic pole position angle alpha based on impulse equality principle i And based on the initial value of alpha i The initial value is subjected to iterative solution,when the program converges, the approximate true solution of the nonlinear overrunning equation set can be obtained, and the magnetic pole structure and the distribution position are obtained, so that the whole rotor magnetic pole structure is obtained according to symmetry;
(4) Simulation verification: simulation verification is carried out 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), and under the condition that the third harmonic current is injected into the winding in addition to the sinusoidal current, the winding interacts with the third harmonic in the air gap flux density to promote electromagnetic torque; and carrying out finite element simulation and verification on the motor with the traditional surface-mounted magnetic pole structure.
2. The design method of claim 1, wherein the iterative solution to the first set of nonlinear equations employs newton's method of iteration.
3. The design method according to claim 1, wherein the first system of nonlinear equations is solved based on the obtained α i And the initial value is used as the initial value of the Matlab fslove solving function to carry out iterative solving.
4. The design method of claim 1, wherein the second set of nonlinear equations is solved iteratively using newton's method of iteration.
5. The design method according to claim 1, wherein the second system of nonlinear equations is solved based on the obtained α i And the initial value is used as the initial value of the Matlab fslove solving function to carry out iterative solving.
6. 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 a current peak value not exceeding the current limit value of the inverter power supply, the optimum value of the current amplitude of the third harmonic injection is 1/6 of the fundamental wave amplitude.
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