WO2023103138A1 - Method for collaborative optimization design of permanent magnet-armature double harmonics of magnetic field-modulated permanent magnet motor - Google Patents

Abstract

Disclosed is a method for collaborative optimization design of permanent magnet-armature double harmonics of a magnetic field-modulated permanent magnet motor. An expression between a flux linkage and a magnetic field harmonic is established according to a harmonic characteristic formula of permanent magnet and armature magnetic fields; and the influence of the flux linkages corresponding to the permanent magnet and armature magnetic field harmonics on torque and power factor is analyzed according to a vector diagram and a power factor expression, so that a collaborative optimization design thought for permanent magnet-armature double harmonics is established. The dimensions of armature magnetic field harmonic optimization objectives and design parameters are reduced by means of sensitivity analysis, experimental point distribution calculation, and independence judgment for an armature magnetic field non-working harmonic; a parameter range constrained by the permanent magnet magnetic field harmonic is taken as a constraint condition to optimize the armature magnetic field harmonic by using a Kriging model and a multi-objective optimization algorithm, so that collaborative optimization design for the permanent magnet-armature magnetic field double harmonics is achieved, thereby improving the torque density and power factor of the motor.

Description

A permanent magnet-armature dual-harmonic collaborative optimization design method for magnetic field modulated permanent magnet motors Technical field

The invention relates to a permanent magnet-armature dual-harmonic collaborative optimization design method for a magnetic field modulation permanent magnet motor, which belongs to the field of motor design and is specifically applicable to motors requiring high torque density and high power factor such as electric vehicles, wind power generation, ship propulsion, etc. system.

Background technique

In recent years, with the rapid development of electric vehicles, wind power generation, ship propulsion and other fields, the current market demand for direct drive motors with higher driving efficiency is increasing. Field modulated permanent magnet motors are characterized by high torque density due to the "field modulation effect". The so-called "magnetic field modulation effect" means that the magnetic field modulation permanent magnet motor modulates and generates a variety of working magnetic field harmonics that can generate torque through the action of its modulation pole, thereby increasing the torque of the motor. Field modulated permanent magnet motors have great development potential in the field of direct drive motors due to their high torque density. However, the magnetic field modulation permanent magnet motor itself has the problem of high flux leakage, which makes the power factor low and restricts its practical application.

At present, the design method to improve the power factor of the magnetic field modulation permanent magnet motor is mainly to increase the permanent magnet flux linkage from the perspective of increasing the permanent magnet magnetic field, or to reduce the armature current from the perspective of reducing the armature magnetic field. The current design method only improves the power factor of the magnetic field modulated permanent magnet motor from a single angle of the permanent magnet magnetic field or the armature magnetic field. From the final result, in some methods, the increase of the power factor will lead to the decrease of the torque density, while some methods Although the power factor of the motor has been improved, the degree of improvement often does not meet expectations, and there is still a large room for improvement. This is mainly because both the permanent magnet magnetic field and the armature magnetic field of the magnetic field modulation permanent magnet motor have an important influence on the power factor of the motor. Ignoring the influence of any magnetic field on the power factor will make the power factor of the magnetic field modulation permanent magnet motor unable to achieve maximum. Therefore, for the magnetic field modulation permanent magnet motor, it is urgent to propose an effective power factor improvement method considering both the permanent magnet and the armature magnetic field.

Contents of the invention

The content of the present invention is to set up the expression between the flux linkage and the magnetic field harmonic according to the harmonic characteristics of the permanent magnet of the magnetic field modulation permanent magnet motor and the armature magnetic field; Expressions for permanent magnet and armature flux linkages to obtain expressions for power factor with respect to permanent magnet and armature field harmonics. According to the vector diagram and the power factor expression, the influence of the flux linkage corresponding to the permanent magnet and armature magnetic field harmonics on the torque and power factor is analyzed, and the permanent magnet-armature double harmonic collaborative optimization design idea is established. Establish the optimization model of the working harmonic amplitude of the synthetic permanent magnetic field with respect to the design parameters, and determine the range of the corresponding design parameters under the limit of the permanent magnetic field harmonics; through sensitivity analysis, calculation of experimental point distribution and non-working harmonics of the armature Independent judgment, reducing the dimension of the armature magnetic field harmonic optimization target and design parameters; using the parameter range after the permanent magnet magnetic field harmonic constraints as constraints, using the kriging model and multi-objective optimization algorithm to The wave is optimized to realize the collaborative optimization design of the permanent magnet-armature magnetic field double harmonic, thereby improving the torque density and power factor of the motor.

Technical scheme of the present invention comprises the following steps:

Step 1: According to the permanent magnet magnetic field harmonic characteristic formula and the armature magnetic field harmonic characteristic formula, establish the expression between the permanent magnet flux linkage with respect to the permanent magnet magnetic field harmonics, and establish the relationship between the armature flux linkage with respect to the armature magnetic field harmonics According to the flux vector diagram of the magnetic field modulation permanent magnet motor, the expression of the power factor with respect to the permanent magnet and armature flux linkage is established, and the expression of the power factor with respect to the harmonics of the permanent magnet and armature magnetic field is obtained. According to the change of the size of the torque working area with the permanent magnet and armature flux linkage in the vector diagram, and combining the above expressions to analyze the influence of the flux linkage corresponding to the harmonics of the permanent magnet and armature magnetic field on the torque and power factor, the permanent magnet and armature flux linkage is established. Magneto-armature double harmonic synergistic optimization design idea to improve the torque density and power factor of the motor;

For the permanent magnetic field harmonics, from the perspective of whether the permanent magnetic field harmonics contribute to the torque, the permanent magnetic field harmonics are divided into two types: permanent magnetic field working harmonics and permanent magnetic field non-working harmonics. The harmonics of the permanent magnetic field that contribute to the torque are the working harmonics of the permanent magnetic field, and the harmonics of the permanent magnetic field that do not contribute to the torque are the non-working harmonics of the permanent magnetic field. The working harmonics of the synthetic permanent magnetic field can be obtained by weighting the working harmonics of the permanent magnetic field. The working harmonic amplitude of the magnetic field can maintain a high torque density while improving the power factor; for the armature magnetic field harmonics, the armature magnetic field There are two types of armature magnetic field working harmonics and armature magnetic field non-working harmonics. The armature magnetic field harmonics that contribute to the torque are the armature magnetic field working harmonics, and the armature magnetic field harmonics that do not contribute to the torque are the armature magnetic field non-working harmonics. According to the flux linkage and power factor expressions, the flux linkage corresponding to the non-working harmonic of the armature magnetic field is inversely proportional to the power factor, and according to the flux linkage phasor diagram, reducing the non-working harmonic of the armature magnetic field will not affect the torque corresponding to The size of the working area, so reducing the non-working harmonics of the armature field can improve the power factor without losing torque density.

According to the analysis of the vector diagram of the motor and the power factor expression, it is determined that under the premise of ensuring that the working harmonic of the synthetic permanent magnet magnetic field is at a high level, the minimum value of the non-working harmonic of the armature magnetic field and the working harmonic of the armature magnetic field are determined. The optimization of the maximum value can realize the collaborative optimization design of the double harmonics of the permanent magnet-armature magnetic field, thereby improving the torque density and power factor of the motor.

Step 2: Limit the working harmonic amplitude of the synthetic permanent magnetic field from the perspective of the permanent magnetic field. Taking the minimum value of the working harmonic amplitude of the synthetic permanent magnetic field as a constraint condition, the design parameters that have a greater impact on the working harmonics of the permanent magnetic field are selected through sensitivity analysis. Based on the high sensitivity to the working harmonics of the permanent magnetic field Design parameters, establish an optimization model for the working harmonics of the synthetic permanent magnetic field, and use the Kriging model to express the relationship between the working harmonic amplitude of the synthetic permanent magnetic field and the design parameters with high sensitivity to the working harmonics of the permanent magnetic field, According to the minimum synthetic permanent magnet magnetic field working harmonic amplitude set in the optimization model, based on the established Kriging model, the corresponding variation range of the design parameters with high sensitivity to the permanent magnetic magnetic field working harmonic is obtained.

Step 3: Simplify the armature field harmonics optimization objective. Since there are many harmonic orders of the armature magnetic field to be optimized, it is necessary to simplify the optimization objectives of the armature magnetic field harmonics and reduce the number of optimization objectives. First, analyze the sensitivity of the armature magnetic field harmonics to the performance of the motor, select the more sensitive armature magnetic field harmonics as the optimization target, and further calculate the distribution of the armature magnetic field harmonics according to the experimental design method. According to the distribution diagram of wave experiment points, the non-operating harmonics of the armature magnetic field with different changing trends of the working harmonics of the armature magnetic field are selected as the harmonics to be optimized, and the simplified optimization target of the armature magnetic field harmonics is obtained by weighting.

Step 4: Independent judgment of non-working harmonics of armature magnetic field. By calculating the interaction effect between the armature magnetic field harmonics, it is analyzed and judged whether there are relatively independent non-working harmonics in the armature magnetic field harmonics. If there are relatively independent non-working harmonics of the armature magnetic field, go to steps 5.1 and 5.2; if there are no relatively independent non-working harmonics of the armature magnetic field, go to step 5.3

Step 5.1: If there are non-operating harmonics of the armature field with relative independence, optimize the non-operating harmonics of the armature field with relative independence separately from the rest of the harmonics of the armature field to reduce the design parameters and optimization objectives dimension to improve the accuracy of the armature field harmonic optimization results. First, optimize the non-working harmonics of the armature magnetic field with relative independence, use sensitivity analysis to select the design parameters that are more sensitive to the non-working harmonics of the armature magnetic field with relative independence, and establish the design parameters with relative Independent Kriging model of non-working harmonics of armature magnetic field. According to the established Kriging model, the optimal design point of non-working harmonics of armature magnetic field with relative independence is selected.

Step 5.2: Optimize the working harmonics of the armature magnetic field and other non-working harmonics of the armature magnetic field that do not have relative independence. Taking the design parameter range limited by the working harmonic amplitude of the synthetic permanent magnet magnetic field as the constraint condition, and taking the working harmonic of the armature magnetic field and the simplified non-working harmonic of the armature magnetic field as the optimization objectives, a multi-objective genetic algorithm is adopted Optimize the working harmonics and non-working harmonics of the motor armature magnetic field, and finally determine the motor design scheme with the optimal armature harmonics on the basis of the high synthetic permanent magnet working harmonic amplitude, and realize the permanent magnet-armature The collaborative optimization design of the double harmonics of the magnetic field improves the torque density and power factor of the motor.

Step 5.3: Optimize the working harmonics and non-working harmonics of the armature magnetic field. Taking the parameter range limited by the working harmonic amplitude of the synthesized permanent magnet magnetic field as the constraint condition, taking the working harmonic of the armature magnetic field and the simplified non-working harmonic of the armature magnetic field as the optimization target, the multi-objective genetic algorithm is used to optimize the The working harmonics and non-working harmonics of the armature magnetic field of the machine are optimized, and finally the design scheme of the motor with the optimal armature harmonics is determined on the basis of the high synthetic permanent magnet working harmonic amplitude. The coordinated optimization design of harmonics can improve the torque density and power factor of the motor.

Further, the expressions of the permanent magnet magnetic field harmonic characteristic formula B _m (θ, t) and the armature magnetic field harmonic characteristic formula B _a (θ, t) in step 1 are:

In the formula, C _m is the Fourier coefficient of the permanent magnetomotive force, D _i and D _j are the Fourier coefficients of the armature magnetomotive force, m is the order of the permanent magnetomotive force, k is the order of the permeability, i and j are the order of the magnetomotive force of the armature, P _r is the number of pole pairs of the permanent magnet, Ω _r is the mechanical speed of the motor, t is the time, Λ ₀ and Λ _k are the Fourier coefficients of the air gap permeance, N _s is the electrical Number of pivot slots. According to the expression, it can be determined that the harmonic order of the permanent magnet magnetic field is mP _r , mP _r ±kN _s , and the harmonic order of the armature magnetic field is i, j, i±kN _s , j±kN _s . F _m (θ,t) is the permanent magnet magnetomotive force expression, Λ _s (θ) is the air gap permeance expression, which can be expressed as:

Further, the expression of the permanent magnet flux linkage on the harmonics of the permanent magnet field in step 1 is:

In the formula, r _g is the air gap radius, l _ef is the axial length, n _c is the number of turns of the winding. Among them, the amplitude expression of the fundamental permanent magnet flux linkage is:

Further, the expression of the armature flux linkage with respect to the harmonics of the armature magnetic field in step 1 is:

Among them, the amplitude expression of the fundamental armature flux linkage is:

Further, the expression of the power factor with respect to the permanent magnet and armature flux linkage in step 1 is:

In the formula,

For flux leakage,

is the permanent magnet flux linkage,

The corresponding flux linkage for the working harmonic of the armature magnetic field,

is the flux linkage corresponding to the non-working harmonic of the armature magnetic field, U and ω _r are the phase voltage and frequency respectively, and E ₀ is the back EMF of the permanent magnet.

Further, the expression of the sensitivity calculation formula in step 2 is:

In the formula, Y(x) represents the harmonic amplitude of the permanent magnet and armature magnetic field under different design parameters, N is the number of samples, and x is the motor design parameter.

The specific steps of the sensitivity analysis in step 2 are as follows: First, use the central composite design sampling method to sample the second-order factor design points, axis points and zero-level center points that meet the second-order regression rotation criterion, providing a basis for the sensitivity calculation. data support. Then, the sensitivity of different design parameters to the working harmonics of the permanent magnetic field is calculated by the sensitivity formula, and the design parameters with greater sensitivity are selected as the design parameters that limit the amplitude of the synthetic permanent magnetic field working harmonics.

The expression of the optimization model of the working harmonic of the synthetic permanent magnetic field established after the sensitivity analysis is:

Constraint:H _sm (x ₂ )>g ₁

In the formula, H _sm is the harmonic amplitude of the synthetic permanent magnet magnetic field of the motor, _x2 represents the design parameter with high sensitivity to the harmonic of the permanent magnet magnetic field of the motor, and H _mh is the working harmonic amplitude of the hth permanent magnet magnetic field value, a _h is the weighting coefficient corresponding to the working harmonic of the permanent magnetic field, g ₁ is the minimum constraint value of the synthetic permanent magnetic field working harmonic.

Further, the simplified optimization target of armature magnetic field harmonics in step 3 is obtained from the sensitivity analysis and the distribution of experimental point distribution of armature magnetic field harmonics. First, the central composite design sampling method is used for sampling to provide data support for the sensitivity calculation. Then, the sensitivity of different armature magnetic field harmonics to power factor is calculated by the sensitivity formula, and the magnetic field harmonic with higher sensitivity is selected as the target of armature harmonic optimization. Further, according to the experimental points in the composite design sampling method, draw the distribution map of the experimental points of the armature magnetic field harmonics, and select the armature with a different trend from the working harmonics of the armature magnetic field according to the changing trend of the different armature magnetic field harmonics in the figure The non-working harmonics of the magnetic field are the harmonics that need to be optimized, and the non-working harmonics of the armature magnetic field that have the same change trend as the working harmonics of the armature magnetic field are not considered as the harmonics that need to be optimized. Then these harmonics that need to be optimized are linearly weighted as optimization targets, reducing the number of optimization targets for armature magnetic field harmonics, and realizing the simplification of armature magnetic field harmonic optimization targets.

Further, the optimized model expression of the non-working harmonics of the armature magnetic field with relative independence in step 5.1 is:

In the formula, _x3 is a design parameter that has a great influence on the non-operating harmonic of the armature magnetic field with relative independence after sensitivity analysis, and _Hal is the non-operating harmonic of the armature magnetic field with relative independence for the lth time, λ _l is the weighting coefficient corresponding to the non-working harmonic of the armature magnetic field with relative independence, and the minimum value of the optimization model is the optimization target.

In step 5.2, the optimized model expression of the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field that do not have relative independence is:

Objectives:

Constraint: f ₁ (x ₂ )>0

In the formula, H _aPr is the working harmonic of the armature magnetic field of the motor P _r , and its maximum value is set as the optimization target, so as to ensure that the optimized motor has a higher torque.

The non-operating harmonics of the armature field are synthesized for the simplified motor, and its minimum value is set as the optimization target. x ₄ represents the remaining design parameters after excluding the design parameter x ₃ from the total design parameters x ₁ , H _as is the sth non-working harmonic of the armature magnetic field, μ _s is the corresponding s-th non-working armature magnetic field Weighting coefficients for harmonics. f ₁ (x ₂ ) is a function of the value range of the design parameters after the working harmonics of the synthetic permanent magnet magnetic field are limited.

Further, the optimized model expressions of the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field in step 5.3 are:

Objectives:

Constraint: f ₁ (x ₂ )>0

In the formula, H _aPr is the working harmonic of the armature magnetic field of the motor P _r , and its maximum value is set as the optimization target, so as to ensure that the optimized motor has a higher torque.

The non-operating harmonics of the armature field are synthesized for the simplified motor, and its minimum value is set as the optimization target. _x1 is the general design parameter of the motor, _x2 is the design parameter with high sensitivity to the harmonic of the permanent magnet field of the motor, H _as is the sth non-working harmonic of the armature magnetic field, μ _s is the corresponding sth electric Weighting factor for non-operating harmonics of the pivot field. f ₁ (x ₂ ) is a function of the value range of the design parameters after the working harmonics of the synthetic permanent magnet magnetic field are limited.

Beneficial effect

After the present invention adopts the above design scheme, it can have the following beneficial effects:

1) The present invention sets up the expression between the flux linkage and the magnetic field harmonic according to the harmonic characteristics of the permanent magnet and the armature magnetic field; Expressions for the chain to obtain expressions for the power factor with respect to the harmonics of the permanent and armature fields. According to the vector diagram and the power factor expression, the influence of the flux linkage corresponding to the permanent magnet and armature magnetic field harmonics on the torque and power factor is analyzed, and the permanent magnet-armature double harmonic collaborative optimization design idea is established, which will be used for the follow-up from permanent magnet The angle of the magnetic and armature double harmonics gives directions for torque density and power factor improvement.

2) The present invention utilizes experimental point distribution calculation, sensitivity analysis and independent judgment of armature magnetic field non-working harmonics to reduce the dimension of optimization objectives and design parameters, further establish the kriging model, and reduce the calculation amount of motor design. Finally, Based on Kriging model and multi-objective optimization algorithm, the optimal design of magnetic field modulation permanent magnet motor is carried out. Compared with the traditional optimization method, the design method of the invention can significantly improve the optimization efficiency and reduce the optimization time.

3) The present invention uses the synthetic permanent magnet magnetic field working harmonic as a constraint condition to obtain the design parameter range satisfying the constraint condition. On this basis, the armature magnetic field harmonic is used as an optimization target to optimize it to realize permanent magnet-armature The angle synergistic optimization design of double harmonics determines the motor design scheme for the optimal armature magnetic field harmonics based on the high synthetic permanent magnetic field working harmonics. Compared with the current method of optimizing power factor solely from the perspective of permanent magnet or armature, the design method of the invention can further improve the torque density and power factor of the motor.

Description of drawings

Fig. 1 is a flow chart of a permanent magnet-armature double harmonic collaborative optimization design method for a magnetic field modulation permanent magnet motor in an embodiment of the present invention;

Fig. 2 is the flux linkage vector diagram of the magnetic field modulation permanent magnet motor of the present invention;

Fig. 3 is the topological structure and parameter distribution diagram of the magnetic field modulation permanent magnet motor of the present invention;

Fig. 4 is the sensitivity analysis result of the design parameters of the magnetic field modulation permanent magnet motor of the present invention about the working harmonic of the synthetic permanent magnet magnetic field;

Fig. 5 (a) is the Kriging model calculation result of the working harmonic of the synthetic permanent magnet magnetic field under the change of w _m , h _m , of the magnetic field modulation permanent magnet motor of the present invention;

Fig. 5(b) is the Kriging model calculation result of the working harmonics of the synthetic permanent magnet magnetic field under the change of _ws , _wp and the magnetic field modulation permanent magnet motor of the present invention;

Fig. 6 (a) is the analysis diagram of the harmonic sensitivity of the armature magnetic field of the magnetic field modulation permanent magnet motor of the present invention;

Fig. 6 (b) is the experimental point distribution figure of magnetic field modulation permanent magnet motor armature magnetic field harmonic of the present invention;

Fig. 7 (a) is the interaction effect diagram between the 1st armature magnetic field non-working harmonic and the 9th armature magnetic field non-working harmonic of the magnetic field modulation permanent magnet motor of the present invention;

Fig. 7 (b) is the interaction effect diagram between the 1st non-working harmonic of the armature magnetic field and the 11 non-working harmonics of the armature magnetic field of the magnetic field modulation permanent magnet motor of the present invention;

Fig. 7 (c) is the interaction effect diagram between the 1st non-working harmonic of the armature magnetic field and the 29 non-working harmonics of the armature magnetic field of the magnetic field modulation permanent magnet motor of the present invention;

Fig. 7 (d) is the interaction effect diagram between the 1st armature magnetic field non-working harmonic and the 31st armature magnetic field working harmonic of the magnetic field modulation permanent magnet motor of the present invention;

Fig. 8 is an analysis diagram of the design parameters of the magnetic field modulation permanent magnet motor of the present invention about the non-working harmonic sensitivity of the primary armature magnetic field with relative independence;

Fig. 9 is a non-working harmonic Kriging model of the primary armature magnetic field with relative independence of the magnetic field modulation permanent magnet motor of the present invention;

Fig. 10 is the distribution diagram of the Pareto frontier of the armature harmonics of the magnetic field modulation permanent magnet motor of the present invention;

Fig. 11 is a comparison chart of torque density and power factor before and after optimization of the magnetic field modulation permanent magnet motor of the present invention.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention.

The embodiments described below by referring to the figures are exemplary only for explaining the present invention and should not be construed as limiting the present invention.

Fig. 1 is a flow chart of a permanent magnet-armature double harmonic collaborative optimization design method for a magnetic field modulation permanent magnet motor in an embodiment of the present invention. Referring to FIG. 1 , a design method for permanent magnet-armature double harmonic collaborative optimization of a magnetic field modulated permanent magnet motor in this embodiment will be described in detail.

A permanent magnet-armature double harmonic collaborative optimization design method for a magnetic field modulation permanent magnet motor according to the present invention, the specific implementation method is shown in Figure 1, including the following steps:

Step 1: According to the harmonic characteristics of the permanent magnet and armature magnetic fields, respectively establish the expressions between the flux linkage and the harmonics of the permanent magnet and armature magnetic fields; according to the magnetic field modulation permanent magnet motor flux vector diagram (Figure 2), establish The expression of the power factor on the permanent magnet and armature flux linkage, according to the change of the size of the torque working area with the permanent magnet and armature flux linkage in the vector diagram, combined with the expression to analyze the corresponding magnetic field of the permanent magnet and armature magnetic field harmonics Based on the influence of the chain on the torque and power factor, the permanent magnet-armature double harmonic collaborative optimization design idea is established to improve the torque density and power factor of the motor.

For the permanent magnetic field harmonics, from the perspective of whether the permanent magnetic field harmonics contribute to the torque, the permanent magnetic field harmonics are divided into two types: permanent magnetic field working harmonics and permanent magnetic field non-working harmonics. The harmonics of the permanent magnetic field that contribute to the torque are the working harmonics of the permanent magnetic field, and the harmonics of the permanent magnetic field that do not contribute to the torque are the non-working harmonics of the permanent magnetic field. The working harmonics of the synthetic permanent magnetic field can be obtained by weighting the working harmonics of the permanent magnetic field. The working harmonic amplitude of the magnetic field can maintain a high torque density while improving the power factor; for the armature magnetic field harmonics, the armature magnetic field There are two types of armature magnetic field working harmonics and armature magnetic field non-working harmonics. The armature magnetic field harmonics that contribute to the torque are the armature magnetic field working harmonics, and the armature magnetic field harmonics that do not contribute to the torque are the armature magnetic field non-working harmonics. According to the flux linkage and power factor expressions, the flux linkage corresponding to the non-working harmonic of the armature magnetic field is inversely proportional to the power factor, and according to the flux linkage phasor diagram, reducing the non-working harmonic of the armature magnetic field will not affect the torque corresponding to The size of the working area, so reducing the non-working harmonics of the armature field can improve the power factor without losing torque density.

According to the analysis of the vector diagram of the motor and the power factor expression, it is determined that under the premise of ensuring that the working harmonic of the synthetic permanent magnet magnetic field is at a high level, the minimum value of the non-working harmonic of the armature magnetic field and the working harmonic of the armature magnetic field are determined. The optimization of the maximum value can realize the collaborative optimization design of the double harmonics of the permanent magnet-armature magnetic field, thereby improving the torque density and power factor of the motor.

Among them, the expressions of the permanent magnet magnetic field harmonic characteristic formula B _m (θ, t) and the armature magnetic field harmonic characteristic formula B _a (θ, t) in step 1 are:

In the formula, C _m is the Fourier coefficient of the permanent magnetomotive force, D _i and D _j are the Fourier coefficients of the armature magnetomotive force, m is the order of the permanent magnetomotive force, k is the order of the permeability, i and j are the order of the magnetomotive force of the armature, P _r is the number of pole pairs of the permanent magnet, Ω _r is the mechanical speed of the motor, t is the time, Λ ₀ and Λ _k are the Fourier coefficients of the air gap permeance, N _s is the electrical Number of pivot slots. According to the expression, it can be determined that the harmonic order of the permanent magnet magnetic field is mP _r , mP _r ±kN _s , and the harmonic order of the armature magnetic field is i, j, i±kN _s , j±kN _s . F _m (θ,t) is the permanent magnet magnetomotive force expression, Λ _s (θ) is the air gap permeance expression, which can be expressed as:

Further, the expression of the permanent magnet flux linkage on the harmonics of the permanent magnet field in step 1 is:

In the formula, r _g is the air gap radius, l _ef is the axial length, n _c is the number of turns of the winding. Among them, the amplitude expression of the fundamental permanent magnet flux linkage is:

In the formula, C ₁ is the Fourier coefficient of the fundamental wave of the permanent magnetomotive force.

Further, the expression of the armature flux linkage with respect to the harmonics of the armature magnetic field in step 1 is:

Among them, the amplitude expression of the fundamental armature flux linkage is:

Further, the expression of the power factor with respect to the permanent magnet and armature flux linkage in step 1 is:

In the formula,

For flux leakage,

is the permanent magnet flux linkage,

The corresponding flux linkage for the working harmonic of the armature magnetic field,

is the flux linkage corresponding to the non-working harmonic of the armature magnetic field, U and ω _r are the phase voltage and frequency respectively, and E ₀ is the permanent magnet back EMF.

Step 2: Limit the working harmonic amplitude of the synthetic permanent magnetic field from the perspective of the permanent magnetic field. Taking the minimum value of the working harmonic amplitude of the synthetic permanent magnetic field as a constraint condition, the design parameters that have a greater impact on the working harmonics of the permanent magnetic field are selected through sensitivity analysis. Based on the high sensitivity to the working harmonics of the permanent magnetic field Design parameters, establish an optimization model for the working harmonics of the synthetic permanent magnetic field, and use the Kriging model to express the relationship between the working harmonic amplitude of the synthetic permanent magnetic field and the design parameters with high sensitivity to the working harmonics of the permanent magnetic field, According to the minimum synthetic permanent magnet magnetic field working harmonic amplitude set in the optimization model, based on the established Kriging model, the corresponding variation range of the design parameters with high sensitivity to the permanent magnetic magnetic field working harmonic is obtained.

Furthermore, a magnetic field modulation permanent magnet motor is selected as the implementation object of this optimization design (Fig. 3), and the sensitivity calculation formula in step 2 is as follows:

In the formula, Y(x) represents the harmonic amplitude of the permanent magnet and armature magnetic field under different design parameters, N is the sampling number, and x is the motor design parameters, including h _m , w _m , w _p , w _s , w _a , h _b , and w _b .

The specific steps of the sensitivity analysis in step 2 are as follows: First, use the central composite design sampling method to sample the second-order factor design points, axis points and zero-level center points that meet the second-order regression rotation criterion, providing a basis for the sensitivity calculation. data support. Then, the sensitivity of different design parameters to the working harmonics of the permanent magnetic field is calculated through the sensitivity formula, and the design parameters with greater sensitivity are selected as the design parameters that limit the amplitude of the synthetic permanent magnetic field working harmonics.

After the sensitivity analysis, according to the sensitivity analysis results of the parameters corresponding to the working harmonics of the permanent magnetic field (Fig. 4), the optimized model of the synthetic permanent magnetic field working harmonics established by selecting the design parameters with high sensitivity is expressed as:

Constraint:H _sm (x ₂ )>g ₁

x ₂ ∈{w _s ,w _p ,w _m ,h _m }

In the formula, H _sm is the harmonic amplitude of the synthetic permanent magnet magnetic field of the motor, _x2 represents the design parameter with high sensitivity to the harmonic of the permanent magnet magnetic field of the motor, and H _mh is the working harmonic amplitude of the hth permanent magnet magnetic field value, a _h is the weighting coefficient corresponding to the working harmonic of the permanent magnetic field, g ₁ is the minimum constraint value of the synthetic permanent magnetic field working harmonic. Fig. 5 shows the Kriging model of the working harmonics of the synthesized permanent magnet magnetic field of the magnetic field modulated permanent magnet motor according to the embodiment of the present invention.

Step 3: Simplify the armature field harmonics optimization objective. Since there are many harmonic orders of the armature magnetic field to be optimized, it is necessary to simplify the optimization objectives of the armature magnetic field harmonics and reduce the number of optimization objectives. First, analyze the sensitivity of the armature magnetic field harmonics to the performance of the motor, select the more sensitive armature magnetic field harmonics as the optimization target, and further calculate the distribution of the armature magnetic field harmonics according to the experimental design method. According to the distribution diagram of wave experiment points, the non-operating harmonics of the armature magnetic field, which are different from the changing trend of the working harmonics of the armature magnetic field, are selected as the harmonics to be optimized, and the simplified optimization target of the armature magnetic field harmonics is obtained by weighting.

Further, the simplified optimization target of armature magnetic field harmonics in step 3 is obtained from the sensitivity analysis and the distribution of experimental point distribution of armature magnetic field harmonics. First, the central composite design sampling method is used for sampling to provide data support for the sensitivity calculation. Then, the sensitivity of different armature magnetic field harmonics to power factor is calculated by the sensitivity formula (Fig. 6(a)), and the magnetic field harmonic with greater sensitivity is selected as the target of armature harmonic optimization. Further, according to the experimental points in the composite design sampling method, draw the distribution diagram of the experimental points of the armature magnetic field harmonics (Fig. 6(b)), as shown in Fig. 6(b), the 29th non-working harmonic of the armature magnetic The working harmonics of the armature magnetic field have the same change trend, so the 29th non-working harmonics of the armature magnetic field are not used as the optimization target, and the rest of the non-working harmonics of the armature magnetic field are selected as the harmonics that need to be optimized, and then these harmonics are optimized Linear weighting is used as the optimization objective to reduce the number of harmonic optimization objectives of the armature magnetic field, and realize the simplification of the harmonic optimization objectives of the armature magnetic field.

Step 4: Independent judgment of non-working harmonics of armature magnetic field. By calculating the interaction effect between the armature magnetic field harmonics, it is analyzed and judged whether there are relatively independent non-working harmonics in the armature magnetic field harmonics. If there are relatively independent non-working harmonics of the armature magnetic field, go to steps 5.1 and 5.2; if there are no relatively independent non-working harmonics of the armature magnetic field, go to step 5.3. Figure 7 analyzes the interaction effect between the non-operating wave of the primary armature magnetic field and other harmonics of the armature magnetic field of the magnetic field modulated permanent magnet motor. As shown in the figure, the 1st non-working harmonic of the armature magnetic field is independent of other harmonics, so the 1st non-working wave of the armature magnetic field is a relatively independent non-working harmonic of the armature magnetic field.

Step 5.1: Because there is a relatively independent armature magnetic field non-working harmonic, optimize it separately from the rest of the armature magnetic field harmonics to reduce the design parameters and optimize the target dimension, and improve the armature magnetic field harmonic optimization the accuracy of the results. Firstly, optimize the first-order non-working harmonic of the armature magnetic field with relative independence, and use the sensitivity analysis to select the design parameters that are more sensitive to the first-order non-operating harmonic of the armature magnetic field with relative independence, as shown in Fig. As shown in 8, the design parameters h _b and w _b have greater sensitivity, so based on h _b and w _b , the Kriging model of the design parameters with respect to the 1st order non-working harmonic of the armature magnetic field with relative independence is established. As shown in Figure 9, according to the established Kriging model, the optimal design point of non-working harmonics of the armature magnetic field with relative independence is selected.

Among them, the optimized model expression of the non-working harmonics of the armature magnetic field with relative independence in step 5.1 is:

Objectives:Min[λ ₁ H _a1 (x ₃ )]

In the formula, x ₃ is the design parameters h _b and w _b that have a great influence on the non-operating harmonics of the relatively independent armature magnetic field after the sensitivity analysis, and H _a1 is the first relatively independent armature magnetic field Non-working harmonics, λ ₁ is the weighting coefficient corresponding to the relatively independent non-working harmonics of the armature magnetic field, and the minimum value of the optimization model is the optimization target.

Step 5.2: Optimize the working harmonics of the armature magnetic field and other non-working harmonics of the armature magnetic field that do not have relative independence. Taking the design parameter range limited by the working harmonic amplitude of the synthetic permanent magnet magnetic field as the constraint condition, and taking the working harmonic of the armature magnetic field and the simplified non-working harmonic of the armature magnetic field as the optimization objectives, a multi-objective genetic algorithm is adopted The working harmonics and non-working harmonics of the motor armature magnetic field are optimized, and the optimal Pareto frontier diagram of the armature harmonics is obtained (Figure 10), and finally it is determined that there is The motor design scheme with optimal armature harmonics realizes the collaborative optimization design of permanent magnet-armature magnetic field double harmonics, thereby improving the torque density and power factor of the motor. As shown in Figure 11, the torque density of the optimized magnetic field modulation permanent magnet motor increases from 26.2Nm/L to 30.9Nm/L, and the power factor increases from 0.49 to 0.7, which verifies the effectiveness of the proposed optimal design method.

Among them, the optimized model expression of the working harmonics of the armature magnetic field in step 5.2 and the simplified non-working harmonics of the armature magnetic field that do not have relative independence is:

Objectives:Max[H _a31 (x ₄ )],Min[μ ₉ H _a9 (x ₄ )+μ ₁₁ H _a11 (x ₄ )]

Constraint: f ₁ (x ₂ )>0

In the formula, H _aPr is the working harmonic of the armature magnetic field of the motor P _r , and its maximum value is set as the optimization target, so as to ensure that the optimized motor has a higher torque. μ ₉ H _a9 (x ₄ )+μ ₁₁ H _a11 (x ₄ ) is the simplified non-working harmonic of the synthesized armature magnetic field of the motor, and its minimum value is set as the optimization target. x ₄ represents the remaining design parameters w _s , w _p , w _m , w _a , _{h m} after excluding the design parameter _{x 3 from} the total design parameters x 1, H _a9 and H _a11 are the 9th and 11th times The non-working harmonics of the armature magnetic field, μ ₉ and μ ₁₁ are the weighting coefficients corresponding to the 9th and 11th non-working harmonics of the armature magnetic field. H _a31 is the 31st working harmonic of the armature magnetic field, and μ ₃₁ is the weighting coefficient corresponding to the 31st working harmonic of the armature magnetic field. f ₁ (x ₂ ) is a function of the value range of the design parameters after the working harmonics of the synthetic permanent magnet magnetic field are limited.

In the description of this specification, references to the terms "one embodiment," "some embodiments," "exemplary embodiments," "example," "specific examples," or "some examples" are intended to mean that the implementation A specific feature, structure, material, or characteristic described by an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications, substitutions and modifications can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the invention is defined by the claims and their equivalents.

Claims (9)

1. A permanent magnet-armature dual-harmonic collaborative optimization design method for a magnetic field modulated permanent magnet motor, characterized in that it comprises the following steps:

   Step 1: According to the permanent magnet magnetic field harmonic characteristic formula and the armature magnetic field harmonic characteristic formula, establish the expression between the permanent magnet flux linkage with respect to the permanent magnet magnetic field harmonics, and establish the relationship between the armature flux linkage with respect to the armature magnetic field harmonics The expression between; according to the magnetic field modulation permanent magnet motor flux vector diagram, establish the expression of the power factor about the permanent magnet and armature flux linkage, and obtain the expression of the power factor about the permanent magnet and armature magnetic field harmonics, according to the vector diagram The size of the medium torque working area varies with the flux linkage of the permanent magnet and the armature. At the same time, combining the above expressions, the influence of the flux linkage corresponding to the harmonics of the permanent magnet and armature magnetic field on the torque and power factor is analyzed, and the permanent magnet-electric The design idea of double-harmonic synergistic optimization improves the torque density and power factor of the motor;

   For the permanent magnetic field harmonics, from the perspective of whether the permanent magnetic field harmonics contribute to the torque, the permanent magnetic field harmonics are divided into two types: permanent magnetic field working harmonics and permanent magnetic field non-working harmonics; The harmonics of the permanent magnetic field that contribute to the torque are the working harmonics of the permanent magnetic field, and the harmonics of the permanent magnetic field that do not contribute to the torque are the non-working harmonics of the permanent magnetic field. The working harmonics of the synthetic permanent magnetic field can be obtained by weighting the working harmonics of the permanent magnetic field. The working harmonic amplitude of the magnetic field can maintain a high torque density while improving the power factor; for the armature magnetic field harmonics, the armature magnetic field There are two types of armature magnetic field working harmonics and armature magnetic field non-working harmonics; the armature magnetic field harmonics that contribute to the torque are the armature magnetic field working harmonics, and the armature magnetic field harmonics that do not contribute to the torque are the armature magnetic field harmonics. The pivot magnetic field is non-working harmonic. According to the flux linkage and power factor expressions, the flux linkage corresponding to the non-working harmonic of the armature magnetic field is inversely proportional to the power factor, and according to the flux linkage phasor diagram, reducing the non-working harmonic of the armature magnetic field will not affect the torque corresponding to The size of the working area, so reducing the non-working harmonics of the armature magnetic field can improve the power factor without losing the torque density;

   According to the analysis of the vector diagram of the motor and the power factor expression, it is determined that under the premise of ensuring that the working harmonic of the synthetic permanent magnet magnetic field is at a high level, the minimum value of the non-working harmonic of the armature magnetic field and the working harmonic of the armature magnetic field are determined. The optimization of the maximum value can realize the collaborative optimization design of the double harmonics of the permanent magnet-armature magnetic field, thereby improving the torque density and power factor of the motor;

   Step 2: Limit the working harmonic amplitude of the synthetic permanent magnetic field from the perspective of the permanent magnetic field, take the minimum value of the working harmonic amplitude of the synthetic permanent magnetic field as a constraint condition, and select the working harmonic amplitude of the permanent magnetic field through sensitivity analysis Harmonics have a greater influence on the design parameters, based on the design parameters with high sensitivity to the permanent magnetic field working harmonics, an optimization model for the synthetic permanent magnetic field working harmonics is established, and the Kriging model is used to represent the synthetic permanent magnetic field working harmonics The relationship between the amplitude and the design parameters with high sensitivity to the working harmonics of the permanent magnetic field, according to the minimum synthetic permanent magnetic field working harmonic amplitude set in the optimization model, is obtained based on the established Kriging model Corresponding to the variation range of design parameters with high sensitivity to the working harmonics of the permanent magnetic field;

   Step 3: Simplify the optimization target of the armature magnetic field harmonics. Since there are many harmonic orders of the armature magnetic field to be optimized, it is necessary to simplify the optimization target of the armature magnetic field harmonics and reduce the number of optimization targets; first, analyze the armature magnetic field The sensitivity of harmonics to motor performance, select the more sensitive armature magnetic field harmonics as the optimization target, and further calculate the distribution of armature magnetic field harmonics according to the experimental design method, through the armature magnetic field harmonic experimental point distribution map, The non-working harmonics of the armature magnetic field with different changing trends of the working harmonics of the armature magnetic field are selected as the harmonics to be optimized, and the simplified optimization target of the armature magnetic field harmonics is obtained by weighting;

   Step 4: Independent judgment of non-working harmonics of armature magnetic field. By calculating the interaction effect between the armature magnetic field harmonics, it is analyzed and judged whether there are relatively independent non-working harmonics in the armature magnetic field harmonics. If there are relatively independent non-working harmonics of the armature magnetic field, go to steps 5.1 and 5.2; if there are no relatively independent non-working harmonics of the armature magnetic field, go to step 5.3

   Step 5.1: If there are non-operating harmonics of the armature field with relative independence, optimize the non-operating harmonics of the armature field with relative independence separately from the rest of the harmonics of the armature field to reduce the design parameters and optimization objectives dimension to improve the accuracy of the optimization results of armature magnetic field harmonics; firstly, optimize the relatively independent armature magnetic field non-working For design parameters with high sensitivity, establish the Kriging model of the design parameters about the non-working harmonic of the armature magnetic field with relative independence, and select the non-working armature magnetic field with relative independence according to the established Kriging model The optimal design point for harmonics;

   Step 5.2: optimize the working harmonics of the armature magnetic field and other non-working harmonics of the armature magnetic field that do not have relative independence, and use the range of design parameters limited by the amplitude of the working harmonics of the synthesized permanent magnetic field as a constraint condition, Taking the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field as optimization targets, the multi-objective genetic algorithm is used to optimize the working harmonics and non-working harmonics of the armature magnetic field of the motor, and finally determine the The motor design scheme with the optimal armature harmonics based on the synthetic permanent magnet working harmonic amplitude, realizes the collaborative optimization design of the permanent magnet-armature magnetic field double harmonics, thereby improving the torque density and power factor of the motor;

   Step 5.3: Optimize the working harmonics and non-working harmonics of the armature magnetic field. Taking the parameter range limited by the working harmonic amplitude of the synthesized permanent magnet magnetic field as the constraint condition, taking the working harmonic of the armature magnetic field and the simplified non-working harmonic of the armature magnetic field as the optimization target, the multi-objective genetic algorithm is used to optimize the The working harmonics and non-working harmonics of the armature magnetic field of the machine are optimized, and finally the design scheme of the motor with the optimal armature harmonics is determined on the basis of the high synthetic permanent magnet working harmonic amplitude. The coordinated optimization design of harmonics can improve the torque density and power factor of the motor.
2. According to the magnetic field modulation permanent magnet motor permanent magnet-armature double harmonic collaborative optimization design method of claim 1, it is characterized in that, in step 1, the permanent magnet magnetic field harmonic characteristic formula B _m (θ, t) and the armature magnetic field harmonic The wave characteristic formula B _a (θ,t) is:

   

   

   In the formula, C _m is the Fourier coefficient of the permanent magnetomotive force, D _i and D _j are the Fourier coefficients of the armature magnetomotive force, m is the order of the permanent magnetomotive force, k is the order of the permeability, i and j are the order of the magnetomotive force of the armature, P _r is the number of pole pairs of the permanent magnet, Ω _r is the mechanical speed of the motor, t is the time, Λ ₀ and Λ _k are the Fourier coefficients of the air gap permeance, N _s is the electrical According to the number of pivot slots, the harmonic order of the permanent magnet magnetic field can be determined as mP _r , mP _r ±kN _s , and the harmonic order of the armature magnetic field is i, j, i±kN _s , j±kN _s , F _a (θ,t) is the armature magnetomotive force; F _m (θ,t) is the permanent magnet magnetomotive force expression, Λ _s (θ) is the air gap permeance expression, which can be expressed as:

   

   
3. According to claim 1, the permanent magnet-armature double harmonic collaborative optimization design method for magnetic field modulation permanent magnet motor is characterized in that, in step 1, the expression of the permanent magnet flux linkage with respect to the permanent magnet magnetic field harmonic is:

   

   In the formula, r _g is the radius of the air gap, l _ef is the axial length, n _c is the number of turns of the winding; where, the expression of the amplitude of the fundamental permanent magnet flux linkage is:

   

   In the formula, C ₁ is the Fourier coefficient of the fundamental wave of the permanent magnetomotive force.
4. According to claim 1, the permanent magnet-armature double harmonic collaborative optimization design method for magnetic field modulation permanent magnet motor is characterized in that the expression of armature flux linkage in step 1 with respect to armature magnetic field harmonics is:

   

   Among them, the amplitude expression of the fundamental armature flux linkage is:

   
5. According to claim 1, the permanent magnet-armature dual-harmonic collaborative optimization design method for magnetic field modulation permanent magnet motor is characterized in that, in step 1, the expression of the power factor with respect to the permanent magnet and armature flux linkage is:

   

   In the formula,

   

   For flux leakage,

   

   is the permanent magnet flux linkage,

   

   The corresponding flux linkage for the working harmonic of the armature magnetic field,

   

   is the flux linkage corresponding to the non-working harmonic of the armature magnetic field, U and ω _r are the phase voltage and frequency respectively, and E ₀ is the back EMF of the permanent magnet.
6. According to claim 1, the permanent magnet-armature dual-harmonic collaborative optimization design method for magnetic field modulation permanent magnet motor is characterized in that, the sensitivity calculation formula in step 2 is expressed as:

   

   In the formula, Y(x) represents the harmonic amplitude of the permanent magnet and armature magnetic field under different design parameters, N is the sampling number, and x is the motor design parameter;

   The specific steps of the sensitivity analysis in step 2 are as follows: First, use the central composite design sampling method to sample the second-order factor design points, axis points and zero-level center points that meet the second-order regression rotation criterion, providing a basis for the sensitivity calculation. Data support; then, the sensitivity of different design parameters to the working harmonics of the permanent magnetic field is calculated through the sensitivity formula, and the design parameters with greater sensitivity are selected as the design parameters that limit the amplitude of the synthetic permanent magnetic field working harmonics;

   The expression of the optimization model of the working harmonic of the synthetic permanent magnetic field established after the sensitivity analysis is:

   

   Constraint:H _sm (x ₂ )>g ₁

   In the formula, H _sm is the harmonic amplitude of the synthetic permanent magnet magnetic field of the motor, _x2 represents the design parameter with high sensitivity to the harmonic of the permanent magnet magnetic field of the motor, and H _mh is the working harmonic amplitude of the hth permanent magnet magnetic field value, a _h is the weighting coefficient corresponding to the working harmonic of the permanent magnetic field, g ₁ is the minimum constraint value of the synthetic permanent magnetic field working harmonic.
7. According to the magnetic field modulation permanent magnet motor permanent magnet-armature double harmonic collaborative optimization design method of claim 1, it is characterized in that, in step 3, the armature magnetic field harmonic optimization target after simplification is determined by sensitivity analysis and armature magnetic field harmonic First, use the central composite design sampling method to sample to provide data support for the sensitivity calculation; then, use the sensitivity formula to calculate the sensitivity of different armature magnetic field harmonics to the power factor, and choose a higher sensitivity The magnetic field harmonics of the armature are used as the optimization target of the armature harmonics; further, according to the experimental points in the composite design sampling method, the distribution map of the experimental point distribution of the armature magnetic field harmonics is drawn, and according to the change trend of different armature magnetic field harmonics in the figure, the The non-working harmonics of the armature magnetic field with different changing trends of the working harmonics of the armature magnetic field are the harmonics that need to be optimized, while the non-working harmonics of the armature magnetic field that have the same changing trend as the working harmonics of the armature magnetic field are not considered as the harmonics that need to be optimized ; Then these harmonics that need to be optimized are linearly weighted as optimization targets, reducing the number of optimization targets for armature magnetic field harmonics, and realizing the simplification of the optimization targets for armature magnetic field harmonics.
8. According to claim 1, the permanent magnet-armature dual-harmonic collaborative optimization design method of magnetic field modulation permanent magnet motor is characterized in that, in step 5.1, the optimization model expression of the non-working harmonic of the armature magnetic field having relative independence is:

   

   In the formula, _x3 is a design parameter that has a great influence on the non-operating harmonic of the armature magnetic field with relative independence after sensitivity analysis, and _Hal is the non-operating harmonic of the armature magnetic field with relative independence for the lth time, λ _l is the weighting coefficient corresponding to the non-working harmonic of the armature magnetic field with relative independence, and the minimum value of the optimization model is the optimization goal;

   In step 5.2, the optimized model expression of the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field that do not have relative independence is:

   

   Constraint: f ₁ (x ₂ )>0

   In the formula, H _aPr is the working harmonic of the armature magnetic field of the motor P _r , and its maximum value is set as the optimization target, so as to ensure that the optimized motor has a higher torque,

   

   The non-working harmonic of the armature magnetic field is synthesized for the simplified motor, and its minimum value is set as the optimization target. x ₄ represents the remaining design parameters after excluding the design parameter x ₃ from the total design parameters x ₁ . H _as is the sth non-working harmonic of the armature magnetic field, μ _s is the weighting coefficient corresponding to the s-th non-working armature magnetic field harmonic, and f ₁ (x ₂ ) is the design after limiting the working harmonic of the synthetic permanent magnet magnetic field Parameter value range function.
9. According to claim 1, the permanent magnet-armature double harmonic collaborative optimization design method for magnetic field modulation permanent magnet motor is characterized in that, in step 5.3, the working harmonic of the armature magnetic field and the non-working harmonic of the simplified armature magnetic field The optimization model expression of is:

   

   Constraint: f ₁ (x ₂ )>0

   In the formula, H _aPr is the working harmonic of the armature magnetic field of the motor P _r , and its maximum value is set as the optimization target, so as to ensure that the optimized motor has a higher torque;

   

   The non-working harmonics of the armature magnetic field are synthesized for the simplified motor, and its minimum value is set as the optimization target; x ₁ is the overall design parameter of the motor, and x ₂ indicates that it is highly sensitive to the harmonics of the permanent magnet magnetic field of the motor H _as is the sth non-working harmonic of the armature magnetic field, μ _s is the weighting coefficient corresponding to the s-th non-working armature magnetic field harmonic; f ₁ (x ₂ ) is the working harmonic of the synthesized permanent magnet magnetic field Restricted design parameter value range function.

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