Permanent magnet-armature double-harmonic optimization method for a magnetic field-modulated permanent magnet motor

Abstract

A permanent magnet-armature double-harmonic collaborative optimisation design method for a magnetic field modulation permanent magnet motor. Establishing an expression between the flux linkage and the

Description

PERMANENT MAGNET- ARMATURE DOUBLE-HARMONIC COLLABORATIVE OPTIMIZATION DESIGN METHOD FOR MAGNETIC FIELD-MODULATED PERMANENT MAGNET MOTOR TECHNICAL FIELD The present disclosure relates to a permanent magnet-armature double-harmonic collaborative optimization design method for a magnetic field-modulated permanent magnet motor, which belongs to the motor design field and is particularly applicable to motor systems for electric automobiles, wind power generation, marine propulsion, and the like that require a high torque density and a high power factor. BACKGROUND In recent years, with the rapid development of electric automobiles, wind power generation, marine propulsion, and other fields, there is an increasing demand for direct-drive motors of high driving efficiency in the market. A magnetic field-modulated permanent magnet motor features a high torque density due to the "magnetic field modulation effect". The "magnetic field modulation effect” indicates that the magnetic field-modulated permanent magnet motor produces, with its modulation poles, a variety of working magnetic field harmonics that can generate torque, thereby increasing the torque of the motor. The magnetic field-modulated permanent magnet motor with a high torque density has a huge development potential in the field of direct-drive motors. However, the magnetic field-modulated permanent magnet motor has the problem of high magnetic flux leakage, which results in a low power factor and limits the practical application of the motor. At present, design methods for increasing the power factor of the magnetic field-modulated permanent magnet motor are mainly increasing the permanent magnet flux linkages from the aspect of the permanent magnetic field or reducing the armature current from the aspect of the armature magnetic field. The current design methods merely increase the power factor of the magnetic field- modulated permanent magnet motor from the aspect of the permanent magnetic field or the armature magnetic field alone, and the final results show that in some methods, the increase of the power factor leads to a decrease of the torque density while in some other methods, the degree of the increase in the power factor of the motor is not desirable and improvements can still be made. The main reason is that both the permanent magnetic field and the armature magnetic field of the magnetic field-modulated permanent magnet motor have an important influence on the power factor of the motor, and the maximum power factor of the magnetic field-modulated permanent magnet motor cannot be reached if the influence of any one of the magnetic fields on the power factor is ignored. Therefore, it is in urgent need of an effective method for increasing the power factor of the magnetic field-modulated permanent magnet motor from the aspect of both the permanent magnet and the armature magnetic field. SUMMARY According to the present disclosure, expressions of flux linkages in relation to magnetic field harmonics are established according to harmonic characteristics of permanent magnet and armature magnetic fields of a magnetic field-modulated permanent magnet motor. An expression of a power factor in relation to the permanent magnet and armature flux linkages is established according to a flux linkage vector diagram of the magnetic field-modulated permanent magnet motor, and an expression of the power factor in relation to the permanent magnet and armature magnetic field harmonics is obtained. Influences of the flux linkages corresponding to the permanent magnet and armature magnetic field harmonics on torque and the power factor are analyzed according to the vector diagram and the power factor expression, and permanent magnet-armature double-harmonic collaborative optimization design thoughts are established. An optimization model of an amplitude of synthesized working harmonics of the permanent magnetic field in relation to design parameters is built, and a corresponding design parameter range limited by the permanent magnetic field harmonics is determined. Dimensions of optimization objectives and design parameters of the armature magnetic field harmonics are reduced through sensitivity analysis, experimental point distribution calculation, and independence judgment on non-working harmonics of the armature magnetic field. A parameter range limited by the permanent magnetic field harmonics is taken as a constraint, and the armature magnetic field harmonics are optimized by using a Kriging model and a multi-objective optimization algorithm to realize the permanent magnet-armature magnetic field double-harmonic collaborative optimization design and improve the torque density and the power factor of the motor. The technical solution of the present disclosure includes the following steps: step 1: establishing an expression of permanent magnet flux linkages in relation to permanent magnetic field harmonics and establishing an expression of armature flux linkages in relation to armature magnetic field harmonics according to a harmonic characteristic formula of a permanent magnetic field and a harmonic characteristic formula of an armature magnetic field, respectively; establishing an expression of a power factor in relation to the permanent magnet and armature flux linkages according to a flux linkage vector diagram of the magnetic field-modulated permanent magnet motor and obtaining an expression of the power factor in relation to the permanent magnet and armature magnetic field harmonics; analyzing, through the expression, influences of the flux linkages corresponding to the permanent magnet and armature magnetic field harmonics on torque and the power factor according to changes in size of a torque working area along with the permanent magnet and armature flux linkages in the vector diagram, and establishing permanent magnet- armature double-harmonic collaborative optimization design thoughts to improve a torque density and the power factor of the motor; dividing the permanent magnetic field harmonics into working harmonics of the permanent magnetic field and non-working harmonics of the permanent magnetic field based on whether the permanent magnetic field harmonics contribute to the torque, where the permanent magnetic field harmonics contributing to the torque are working harmonics of the permanent magnetic field, and the permanent magnetic field harmonics not contributing to the torque are non-working harmonics of the permanent magnetic field; weighting the working harmonics of the permanent magnetic field in each order to obtain synthesized working harmonics of the permanent magnetic field, where the permanent magnet flux linkages corresponding to the synthesized working harmonics of the permanent magnetic field are directly proportional to the torque and the power factor, so that when an amplitude of the synthesized working harmonics of the permanent magnetic field is enlarged, the power factor is increased and the torque density remains high; dividing the armature magnetic field harmonics into working harmonics of the armature magnetic field and non-working harmonics of the armature magnetic field based on whether the armature magnetic field harmonics contribute to the torque, where the armature magnetic field harmonics contributing to the torque are working harmonics of the armature magnetic field, and the armature magnetic field harmonics not contributing to the torque are non-working harmonics of the armature magnetic field; the flux linkages corresponding to the non-working harmonics of the armature magnetic field are inversely proportional to the power factor according to the expression of the flux linkages and the power factor; meanwhile, according to the flux linkage vector diagram, a decrease in the non-working harmonics of the armature magnetic field does not influence the size of the corresponding torque working area, so that the non-working harmonics of the armature magnetic field are decreased to increase the power factor without reducing the torque density; determining, according to analysis of the vector diagram and the power factor expression of the motor, that when the synthesized working harmonics of the permanent magnetic field at a high level are ensured, a minimum value of the non-working harmonics of the armature magnetic field and a maximum value of the working harmonics of the armature magnetic field are optimized to realize the permanent magnet-armature magnetic field double-harmonic collaborative optimization design and improve the torque density and the power factor of the motor; step 2: limiting the amplitude of the synthesized working harmonics of the permanent magnetic field, where a minimum value of the amplitude of the synthesized working harmonics of the permanent magnetic field is taken as a constraint, and design parameters having great influences on the working harmonics of the permanent magnetic field are selected through sensitivity analysis; an optimization model of the synthesized working harmonics of the permanent magnetic field is built based on the design parameters highly sensitive to the working harmonics of the permanent magnetic field; a relationship between the amplitude of the synthesized working harmonics of the permanent magnetic field and the design parameters highly sensitive to the working harmonics of the permanent magnetic field is expressed by using a Kriging model; a corresponding variation range of the design parameters highly sensitive to the working harmonics of the permanent magnetic field is obtained based on the built Kriging model according to the set minimum amplitude of the synthesized working harmonics of the permanent magnetic field in the optimization model; step 3: simplifying armature magnetic field harmonic optimization objectives, where since the armature magnetic field harmonics in a large number of orders are to be optimized, the armature magnetic field harmonic optimization objectives need to be simplified to reduce the number of the optimization objectives; sensitivity of the armature magnetic field harmonics to motor performance is analyzed and the highly sensitive armature magnetic field harmonics are selected as the optimization objectives; distribution of the armature magnetic field harmonics is calculated according to an experimental design method; the non-working harmonics of the armature magnetic field in a changing trend different from the working harmonics of the armature magnetic field are selected as the harmonics to be optimized according to an experimental point distribution diagram of the armature magnetic field harmonics, and the simplified armature magnetic field harmonic optimization objectives are obtained by weighting; step 4: judging independence of the non-working harmonics of the armature magnetic field, where an interaction effect between the armature magnetic field harmonics is calculated to analyze and judge whether relatively independent non-working harmonics exist in the armature magnetic field harmonics; if the relatively independent non-working harmonics of the armature magnetic field exist, steps 5.1 and 5.2 are performed; and if the relatively independent non-working harmonics of the armature magnetic field do not exist, step 5.3 is performed; step 5.1: if the relatively independent non-working harmonics of the armature magnetic field exist, optimizing the relatively independent non-working harmonics of the armature magnetic field and the remaining armature magnetic field harmonics separately to reduce dimensions of the design parameters and the optimization objectives and increase accuracy of armature magnetic field harmonic optimization results, where the relatively independent non-working harmonics of the armature magnetic field are optimized first, the design parameters highly sensitive to the relatively independent non-working harmonics of the armature magnetic field are selected through sensitivity analysis, a Kriging model of the design parameters in relation to the relatively independent non- working harmonics of the armature magnetic field is built, and an optimal design point of the relatively independent non-working harmonics of the armature magnetic field is selected according to the built Kriging model; step 5.2: optimizing the working harmonics of the armature magnetic field and the remaining not relatively independent non-working harmonics of the armature magnetic field, where a design parameter range limited by the amplitude of the synthesized working harmonics of the permanent magnetic field is taken as a constraint, the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field are taken as the optimization objectives, a multi-objective genetic algorithm is used to optimize the working harmonics and the non-working harmonics of the armature magnetic field of the motor, and a motor design scheme with optimal armature harmonics based on the high amplitude of the synthesized permanent magnet working harmonics is determined to realize the permanent magnet-armature magnetic field double- harmonic collaborative optimization design and improve the torque density and the power factor of the motor; step 5.3: optimizing the working harmonics and the non-working harmonics of the armature magnetic field, where the parameter range limited by the amplitude of the synthesized working harmonics of the permanent magnetic field is taken as a constraint, the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field are taken as the optimization objectives, the multi-objective genetic algorithm is used to optimize the working harmonics and the non-working harmonics of the armature magnetic field of the motor, and a motor design scheme with optimal armature harmonics based on the high amplitude of the synthesized permanent magnet working harmonics is determined to realize the permanent magnet- armature magnetic field double-harmonic collaborative optimization design and improve the torque density and the power factor of the motor. Further, the harmonic characteristic formula of the permanent magnetic field B»(6,f) and the harmonic characteristic formula of the armature magnetic field Ba(6,?) in the step 1 are as follows: B (6,t)=F, (6,t)x A (0) > C,A,cos(mPO-mPQNO+= > > C,A,cos[(mP. £kN,)6 —-mPQ,1] a np THRE Ng ee a m=13,5 m=135.k=1,23 B,(6,t)=F,(6,t)xA, (0) => DA cos(i@+PQ,t)+ > D.A,cos(j6—-PQ,t) 15S DA, costa, 0+ ROA + 2 i k=123. * © 1s >. DA, cos[(j£kN,)0—PQ,] 2 J k=1,2,3 where Cy, is a Fourier coefficient of a permanent magnet magnetomotive force, D; and D; are Fourier coefficients of an armature magnetomotive force, m is an order of the permanent magnet magnetomotive force, k is an order of permeance, i andj are orders of the armature magnetomotive force, P is a number of permanent magnet pole pairs, Q- is a mechanical speed of the motor, 7 is time, Ao and Ay are Fourier coefficients of air-gap permeance, and N; is a number of armature slots; according to the expressions, the permanent magnetic field harmonics are in the orders of mP, and mPr = kN;, and the armature magnetic field harmonics are in the orders of i, j, i = kN;, and j = kN; the permanent magnet magnetomotive force Fi(6,t) and the air-gap permeance As(6) are expressed as follows: F,6,0)= Y C,cos(mP.6-mPQ,t) m=l35, A B)=Ay+ > A, coskN 6 *=123, Further, the expression of the permanent magnet flux linkages in relation to the permanent magnetic field harmonics in the step 1 is as follows: "YB (6,140 ea =rlnf"" B,( 2rl.n C A, = sin Zk mPQ t > m=1,3,5. mP, N, + CA, 2nlyn. z(mP,+kN,) mt £3 _gin———L——"cosmP.Q,t S m=1335.k=123. 2 mP kN, N, where 7g is a radius of an air gap, / eris an axial length, and n. is a number of winding turns; a fundamental amplitude of the permanent magnet flux linkages is expressed as follows: 2rl.n Pp pC, Ze go 7 P N, “+ CA 2m. ah 7 £kN,) > k=1,23. 2 P£tkN, N, Further, the expression of the armature flux linkages in relation to the armature magnetic field harmonics in the step 1 is as follows: xIN, 0,1) e.()=rln | By = 2r ln, i > 2rl.n, j => DA, ede in cosPQt + DA, Zed in 2) cosPOt N "7 7 T N, wil ED DA, 2r ln, Lomi Zo DA, rn, mj Zit Tee en Zk Zee ein 2 eZ Ed Coin — cos BQ, I+, 9. —L EES Csin—Lcos BQ “5s. 2 itkN, NTT S455. 2 jtkN, N, where a fundamental amplitude of the armature flux linkages is expressed as follows: & 2rln - 2rl,n i y, = S DA, Zee sin ZL Sp A, Zee gin ZL N, = °° J N, Tl Miz allel, | TT) + y LE _£9 font» 2 ixkN, N, 035. 2 JjxkN, N, DA ifm; sin ¥ 3 DA, 2rd, nL 2 ithN, N, S435. 2 JjfkN, NWN, Further, the expression of the power factor in relation to the permanent magnet and armature flux linkages in the step 1 is as follows: 2)" 2 PF mers =o [1120 tur 0) U DQ. where ¢, represents magnetic flux leakage, ¢» represents the permanent magnet flux linkages, ¢wa represents the flux linkages corresponding to the working harmonics of the armature magnetic field, pn represents the flux linkages corresponding to the non-working harmonics of the armature magnetic field, Uand w; are respectively phase voltage and frequency, and Eo is a back electromotive force of the permanent magnet. Further, a sensitivity calculation formula in the step 2 is expressed as follows: NY xY(x)=-D xD ¥(x) i Se INS 2x INS r(x) (TY (5) where ¥(x) represents the amplitudes of the permanent magnet and armature magnetic field harmonics under different design parameters, N is a number of samples, and x represents the design parameters of the motor. The sensitivity analysis in the step 2 1s specifically implemented as follows: sampling second- order factor design points, axis points, and zero-level center points in accordance with a second-order regression rotation criterion by using a central composite design sampling method to provide data support for sensitivity calculation; calculating, through the sensitivity formula, the sensitivity of different design parameters to the working harmonics of the permanent magnetic field, and selecting the highly sensitive design parameters to limit the amplitude of the synthesized working harmonics of the permanent magnetic field. After the sensitivity analysis, the built optimization model of the synthesized working harmonics of the permanent magnetic field is expressed as follows: H, => a,H,,(x,) h Constraint: H_,(x,) > g, where Hsm 1s the amplitude of the synthesized working harmonics of the permanent magnetic field of the motor, x2 represents the design parameters highly sensitive to the permanent magnetic field harmonics of the motor, Hy is an amplitude of 4% working harmonics of the permanent magnetic field, a» is a weighting coefficient corresponding to the working harmonics of the permanent magnetic field, and g1 is a minimum constraint value of the synthesized working harmonics of the permanent magnetic field. Further, the simplified armature magnetic field harmonic optimization objectives in the step 3 are obtained through the sensitivity analysis and the experimental point distribution of the armature magnetic field harmonics, where the central composite design sampling method is used for sampling to provide data support for sensitivity calculation; the sensitivity of different armature magnetic field harmonics to the power factor is calculated through the sensitivity formula and the highly sensitive magnetic field harmonics are selected as the armature harmonic optimization objectives; the experimental point distribution diagram of the armature magnetic field harmonics is drawn according to the experimental points in the composite design sampling method; according to changing trends of different armature magnetic field harmonics in the diagram, the non-working harmonics of the armature magnetic field in a changing trend different from the working harmonics of the armature magnetic field are selected as the harmonics to be optimized, and the non-working harmonics of the armature magnetic field in a same changing trend as the working harmonics of the armature magnetic field are not taken as the harmonics to be optimized; and the harmonics to be optimized are linearly weighted to be optimization objectives, so that the number of the armature magnetic field harmonic optimization objectives is reduced for simplification of the armature magnetic field harmonic optimization objectives. Further, the optimization model of the relatively independent non-working harmonics of the armature magnetic field in the step 5.1 is expressed as follows: Objectives : Min[ > 4 Ha(x,)] where x3 represents the design parameters having great influences on the relatively independent non-working harmonics of the armature magnetic field after the sensitivity analysis, Ha represents I* relatively independent non-working harmonics of the armature magnetic field, / ; is a weighting coefficient corresponding to the relatively independent non-working harmonics of the armature magnetic field, and minimum values of the optimization model are optimization objectives. The optimization model of the working harmonics of the armature magnetic field and the simplified remaining not relatively independent non-working harmonics of the armature magnetic field in the step 5.2 is expressed as follows: Objectives : Max[H,, (x)L, Min[ pt, Has(x,)] Constraint: f,(x,) >0 where Harr represents P™" working harmonics of the armature magnetic field of the motor and has maximum values set as optimization objectives, ensuring that the optimized motor has high torque; > MH. Has(x,) represents simplified synthesized non-working harmonics of the armature magnetic field of the motor and has minimum values set as optimization objectives; x4 represents the remaining design parameters after the design parameters x; are excluded from total design parameters x1, Has represents s™ non-working harmonics of the armature magnetic field, and us represents a weighting coefficient corresponding to the s* non-working harmonics of the armature magnetic field; and fi(x2) is a value range function of the design parameters limited by the synthesized working harmonics of the permanent magnetic field. Further, the optimization model of the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field in the step 5.3 is expressed as follows Objectives : Max[H,, (x;)], Min[Y_ pu Hes(x,)] Constraint: f,(x,)>0 where Hep: represents the P,™ working harmonics of the armature magnetic field of the motor and has maximum values set as optimization objectives, ensuring that the optimized motor has high torque; > MH, Has(x;) represents the simplified synthesized non-working harmonics of the armature magnetic field of the motor and has minimum values set as optimization objectives; x1 represents the total design parameters of the motor, x2 represents the design parameters highly sensitive to the permanent magnetic field harmonics of the motor, Has represents the s* non-working harmonics of the armature magnetic field, and us represents the weighting coefficient corresponding to the s* non- working harmonics of the armature magnetic field; and fi(xz) is the value range function of the design parameters limited by the synthesized working harmonics of the permanent magnetic field. Beneficial effects: The present disclosure adopts the above technical solution to achieve the following beneficial effects. 1) According to the present disclosure, expressions of flux linkages in relation to magnetic field harmonics are established according to harmonic characteristics of permanent magnet and armature magnetic fields. An expression of a power factor in relation to the permanent magnet and armature flux linkages is established according to a flux linkage vector diagram of the magnetic field- modulated permanent magnet motor, and an expression of the power factor in relation to the permanent magnet and armature magnetic field harmonics is obtained. Influences of the flux linkages corresponding to the permanent magnet and armature magnetic field harmonics on torque and the power factor are analyzed according to the vector diagram and the power factor expression, and permanent magnet-armature double-harmonic collaborative optimization design thoughts are established for subsequent improvement of the torque density and the power factor by using the permanent magnet and armature double harmonics. 2) According to the present disclosure, dimensions of optimization objectives and design parameters are reduced through experimental point distribution calculation, sensitivity analysis, and independence judgment on non-working harmonics of the armature magnetic field, a Kriging model is further built to reduce the amount of calculation for the motor design, and optimization design is performed on the magnetic field-modulated permanent magnet motor based on the Kriging model and a multi-objective optimization algorithm. Compared with the conventional optimization method, the design method of the present disclosure significantly improves the optimization efficiency and reduces the optimization time. 3) According to the present disclosure, synthesized working harmonics of the permanent magnetic field are taken as a constraint, a design parameter range satisfying the constraint is obtained, and the armature magnetic field harmonics are taken as the optimization objectives to be optimized, thereby realizing the collaborative optimization design by using the permanent magnet and armature double harmonics and determining a motor design scheme with the optimal armature magnetic field harmonics based on the high synthesized working harmonics of the permanent magnetic field. Compared with the existing method of optimizing the power factor from the aspect of the permanent magnet or the armature alone, the design method of the present disclosure can be used to further increase the torque density and the power factor of the motor. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 1s a flow chart of a permanent magnet-armature double-harmonic collaborative optimization design method for a magnetic field-modulated permanent magnet motor in an embodiment of the present disclosure. FIG. 2 is a flux linkage vector diagram of the magnetic field-modulated permanent magnet motor according to the present disclosure. FIG. 3 is a diagram showing the topology and the parameter distribution of the magnetic field- modulated permanent magnet motor according to the present disclosure. FIG. 4 shows sensitivity analysis results of design parameters of the magnetic field-modulated permanent magnet motor in relation to synthesized working harmonics of the permanent magnetic field according to the present disclosure. FIG. 5(a) shows Kriging model calculation results of the synthesized working harmonics of the permanent magnetic field when wn and A» of the magnetic field-modulated permanent magnet motor change according to the present disclosure. FIG. 5(b) shows Kriging model calculation results of the synthesized working harmonics of the permanent magnetic field when ws and w), of the magnetic field-modulated permanent magnet motor change according to the present disclosure. FIG. 6(a) 1s a sensitivity analysis diagram of armature magnetic field harmonics of the magnetic field-modulated permanent magnet motor according to the present disclosure. FIG. 6(b) 1s an experimental point distribution diagram of the armature magnetic field harmonics of the magnetic field-modulated permanent magnet motor according to the present disclosure. FIG. 7(a) is a diagram showing the interaction effect between 1° non-working harmonics of the armature magnetic field and ninth non-working harmonics of the armature magnetic field of the magnetic field-modulated permanent magnet motor according to the present disclosure. FIG. 7(b) is a diagram showing the interaction effect between the 1*' non-working harmonics of the armature magnetic field and eleventh non-working harmonics of the armature magnetic field of the magnetic field-modulated permanent magnet motor according to the present disclosure. FIG. 7(c) is a diagram showing the interaction effect between the 1° non-working harmonics of the armature magnetic field and 29" non-working harmonics of the armature magnetic field of the magnetic field-modulated permanent magnet motor according to the present disclosure. FIG. 7(d) is a diagram showing the interaction effect between the 1* non-working harmonics of the armature magnetic field and 31% working harmonics of the armature magnetic field of the magnetic field-modulated permanent magnet motor according to the present disclosure. FIG. 8 1s a sensitivity analysis diagram of the design parameters of the magnetic field-modulated permanent magnet motor in relation to the 1* relatively independent non-working harmonics of the armature magnetic field according to the present disclosure. FIG. 9 shows a Kriging model of the 1* relatively independent non-working harmonics of the armature magnetic field of the magnetic field-modulated permanent magnet motor according to the present disclosure. FIG. 10 is a Pareto frontier distribution diagram of the armature harmonics of the magnetic field-modulated permanent magnet motor according to the present disclosure. FIG. 11 is a comparison diagram of the torque density and the power factor results before and after optimization of the magnetic field-modulated permanent magnet motor according to the present disclosure. DETAILED DESCRIPTION OF THE EMBODIMENTS The technical solutions of the present disclosure will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present disclosure. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present disclosure, instead of limiting the present disclosure. FIG. 1 1s a flow chart of a permanent magnet-armature double-harmonic collaborative optimization design method for a magnetic field-modulated permanent magnet motor in an embodiment of the present disclosure. Referring to FIG. 1, the permanent magnet-armature double- harmonic collaborative optimization design method for the magnetic field-modulated permanent magnet motor in this embodiment is described in detail. The specific implementation of the permanent magnet-armature double-harmonic collaborative optimization design method for the magnetic field-modulated permanent magnet motor according to the present disclosure is shown in FIG. 1. The method includes the following steps: step 1: Expressions of flux linkages in relation to permanent magnet and armature magnetic field harmonics are established according to harmonic characteristics of permanent magnet and armature magnetic fields, respectively. An expression of a power factor in relation to the permanent magnet and armature flux linkages is established according to a flux linkage vector diagram of the magnetic field-modulated permanent magnet motor (as shown in FIG. 2). Influences of the flux linkages corresponding to the permanent magnet and armature magnetic field harmonics on torque and the power factor are analyzed through the expression according to changes in the size of a torque working area along with the permanent magnet and armature flux linkages in the vector diagram, and permanent magnet-armature double-harmonic collaborative optimization design thoughts are established to improve the torque density and the power factor of the motor. The permanent magnetic field harmonics are divided into working harmonics of the permanent magnetic field and non-working harmonics of the permanent magnetic field based on whether the permanent magnetic field harmonics contribute to the torque. The permanent magnetic field harmonics contributing to the torque are working harmonics of the permanent magnetic field, and the permanent magnetic field harmonics not contributing to the torque are non-working harmonics of the permanent magnetic field. The working harmonics of the permanent magnetic field in each order are weighted to obtain synthesized working harmonics of the permanent magnetic field. The permanent magnet flux linkages corresponding to the synthesized working harmonics of the permanent magnetic field are directly proportional to the torque and the power factor, so that when an amplitude of the synthesized working harmonics of the permanent magnetic field is enlarged, the power factor is increased and the torque density remains high. The armature magnetic field harmonics are divided into working harmonics of the armature magnetic field and non-working harmonics of the armature magnetic field based on whether the armature magnetic field harmonics contribute to the torque. The armature magnetic field harmonics contributing to the torque are working harmonics of the armature magnetic field, and the armature magnetic field harmonics not contributing to the torque are non-working harmonics of the armature magnetic field. The flux linkages corresponding to the non-working harmonics of the armature magnetic field are inversely proportional to the power factor according to the expression of the flux linkages and the power factor. Meanwhile, according to the flux linkage vector diagram, a decrease in the non-working harmonics of the armature magnetic field does not influence the size of the corresponding torque working area, so that the non-working harmonics of the armature magnetic field are decreased to increase the power factor without reducing the torque density. It is determined according to analysis of the vector diagram and the power factor expression of the motor that, when the synthesized working harmonics of the permanent magnetic field at a high level are ensured, a minimum value of the non-working harmonics of the armature magnetic field and a maximum value of the working harmonics of the armature magnetic field are optimized to realize the permanent magnet-armature magnetic field double-harmonic collaborative optimization design and improve the torque density and the power factor of the motor. The harmonic characteristic formula of the permanent magnetic field B»(6,7) and the harmonic characteristic formula of the armature magnetic field B4(6,?) in the step 1 are expressed as follows: B (6,t)=F, (6,t)x A (0) > C,A,cos(mPO-mPQNO+= > > C,A,cos[(mP. £kN,)6 —-mPQ,1] a np THRE Ng ee a m=13,5 m=135.k=1,23 B,(6,t)=F,(6,t)xA, (0) => DA cos(i@+PQ,1)+ > DA cos(j6—PQ,1) is > DA, cos[(i+kN,)0+PQ1]+ 2 i k=123 * 1 wo wo => > DA, cos[(j£AN,)0—PQ,1 2 J k=1,2,3 where Cy, is a Fourier coefficient of a permanent magnet magnetomotive force, D; and D; are Fourier coefficients of an armature magnetomotive force, m is an order of the permanent magnet magnetomotive force, k is an order of permeance, 7 andj are orders of the armature magnetomotive force, Pr is a number of permanent magnet pole pairs, Q- is a mechanical speed of the motor, 7 is time, Ao and A are Fourier coefficients of air-gap permeance, and N; is a number of armature slots. According to the expressions, the permanent magnetic field harmonics are in the orders of mP, and mP: = kN, and the armature magnetic field harmonics are in the orders of 7, / , i = Ns, and j + kN;. The permanent magnet magnetomotive force F»(6,) and the air-gap permeance As(6) are expressed as follows F.(6,n= > C,cos(mP,8-mPQ,t) m=1,3,5. A@)=Ay+ D> A coskN 6 *=123, Further, the expression of the permanent magnet flux linkages in relation to the permanent magnetic field harmonics in the step 1 is as follows: AIN, CL @0=rlnf" " B,( 2r ln C A, 2 in ZB vn mPQ t > m=1,3,5. mP, N, CC, A, + Cute Wily AB ERN) py nk £4 — > m=13.5..k=1.23. 2 mP kN, N, where 7; is a radius of an air gap, / eris an axial length, and #. is a number of winding turns. A fundamental amplitude of the permanent magnet flux linkages is expressed as follows: 2r ln, Ym = Ca, re in ZR P N, 7(P.£kN,) + CA, 2rl CA, 26h 7B £RN,) > k=1,23. 2 PtkN, N, where Ci 1s a fundamental Fourier coefficient of the permanent magnet magnetomotive force. Further, the expression of the armature flux linkages in relation to the armature magnetic field harmonics in the step 1 is as follows: IN, "™ B (6,14dt e.)=rln[ B & i & 2rin, mj => DA, 2M in cos + DA, Zee in cosPOt N "7 T N, wil ED DA, 2rlm, . mi & & DA 2m, nj bt sin—cos BQ, f+. > le RY sin—=cos LQ, iE. 2 ixkN, ON, TT S435 2 jtkN, ON, where a fundamental amplitude of the armature flux linkages is expressed as follows: & 2rl.n i & 2r,l.n i y, = S DA, Zee gin ZL Sp A, Lee gin ZL N, = °° J N, Al oo oo Hild Ll bell. | WT] +> Sy Ed fin —+% » 2 itkN, N, 5,35. 2 JtkN, N, Bunz td AI 0 2 izkN, N, S83. 2 JjtRN, ON, Further, the expression of the power factor in relation to the permanent magnet and armature flux linkages in the step 1 is as follows: 2) 2 E CRIRIANY PF=cosf=22=|1+ —eee where ¢, represents magnetic flux leakage, ¢ represents the permanent magnet flux linkages, @wa represents the flux linkages corresponding to the working harmonics of the armature magnetic field, pn represents the flux linkages corresponding to the non-working harmonics of the armature magnetic field, U and w- are respectively phase voltage and frequency, and Ep is a back electromotive force of the permanent magnet. step 2: The amplitude of the synthesized working harmonics of the permanent magnetic field is limited. A minimum value of the amplitude of the synthesized working harmonics of the permanent magnetic field is taken as a constraint, and design parameters having great influences on the working harmonics of the permanent magnetic field are selected through sensitivity analysis. An optimization model of the synthesized working harmonics of the permanent magnetic field is built based on the design parameters highly sensitive to the working harmonics of the permanent magnetic field. The relationship between the amplitude of the synthesized working harmonics of the permanent magnetic field and the design parameters highly sensitive to the working harmonics of the permanent magnetic field is expressed by using a Kriging model. A corresponding variation range of the design parameters highly sensitive to the working harmonics of the permanent magnetic field is obtained based on the built Kriging model according to the set minimum amplitude of the synthesized working harmonics of the permanent magnetic field in the optimization model. Further, a magnetic field-modulated permanent magnet motor is selected to receive the optimization design (as shown in FIG. 3), and a sensitivity calculation formula in the step 2 is expressed as follows: Sey NY xY (x)= xD Y(x) ym M2 xXYI- xp (x) WWE =P Wr) - Cr) where ¥(x) represents the amplitudes of the permanent magnet and armature magnetic field harmonics under different design parameters, N is a number of samples, and x represents the design parameters of the motor including Am, Wm, Wp, Ws, Wa, hs, and ws. The sensitivity analysis in the step 2 is specifically implemented as follows: Second-order factor design points, axis points, and zero-level center points in accordance with a second-order regression rotation criterion are sampled by using a central composite design sampling method to provide data support for sensitivity calculation. The sensitivity of different design parameters to the working harmonics of the permanent magnetic field is calculated through the sensitivity formula, and the highly sensitive design parameters are selected to limit the amplitude of the synthesized working harmonics of the permanent magnetic field. After the sensitivity analysis, the design parameters of high sensitivity are selected according to the sensitivity analysis results of the parameters corresponding to the working harmonics of the permanent magnetic field (as shown in FIG. 4) to build the optimization model of the synthesized working harmonics of the permanent magnetic field. The optimization model is expressed as follows: H, = aH, (x,) =a,H, +a H, +a,H, +a, H,; h Constraint: H, (x,) > g; x, € {Wow wh} where Hip is the amplitude of the synthesized working harmonics of the permanent magnetic field of the motor, x represents the design parameters highly sensitive to the permanent magnetic field harmonics of the motor, Hu is an amplitude of 4% working harmonics of the permanent magnetic field, a» is a weighting coefficient corresponding to the working harmonics of the permanent magnetic field, and gi is a minimum constraint value of the synthesized working harmonics of the permanent magnetic field. FIG. 5 shows the Kriging model of the synthesized working harmonics of the permanent magnetic field of the magnetic field-modulated permanent ‘magnet motor in the embodiment of the present disclosure. step 3: Armature magnetic field harmonic optimization objectives are simplified. Since the armature magnetic field harmonics in a large number of orders are to be optimized, the armature magnetic field harmonic optimization objectives need to be simplified to reduce the number of the optimization objectives. The sensitivity of the armature magnetic field harmonics to motor performance is analyzed and the highly sensitive armature magnetic field harmonics are selected as the optimization objectives. The distribution of the armature magnetic field harmonics is calculated according to an experimental design method. The non-working harmonics of the armature magnetic field in a changing trend different from the working harmonics of the armature magnetic field are selected as the harmonics to be optimized according to an experimental point distribution diagram of the armature magnetic field harmonics, and the simplified armature magnetic field harmonic optimization objectives are obtained by weighting. Further, the simplified armature magnetic field harmonic optimization objectives in the step 3 are obtained through the sensitivity analysis and the experimental point distribution of the armature magnetic field harmonics. The central composite design sampling method is used for sampling to provide data support for sensitivity calculation. The sensitivity of different armature magnetic field harmonics to the power factor is calculated through the sensitivity formula (as shown in FIG. 6(a)), and the highly sensitive magnetic field harmonics are selected as the armature harmonic optimization objectives. The experimental point distribution diagram of the armature magnetic field harmonics (as shown in FIG. 6(b)) is drawn according to the experimental points in the composite design sampling method. As shown in FIG. 6(b), the 29 non-working harmonics of the armature magnetic field and the 31% working harmonics of the armature magnetic field have the same changing trend. Therefore, the 29" non-working harmonics of the armature magnetic field are not taken as optimization objectives, and the remaining non-working harmonics of the armature magnetic field are selected as harmonics to be optimized and are linearly weighted to be optimization objectives, so that the number of the armature magnetic field harmonic optimization objectives is reduced for simplification of the armature magnetic field harmonic optimization objectives. step 4: The independence of the non-working harmonics of the armature magnetic field is judged. An interaction effect between the armature magnetic field harmonics is calculated to analyze and judge whether relatively independent non-working harmonics exist in the armature magnetic field harmonics. If the relatively independent non-working harmonics of the armature magnetic field exist, steps 5.1 and 5.2 are performed; and if the relatively independent non-working harmonics of the armature magnetic field do not exist, step 5.3 is performed. FIG. 7 analyzes the interaction effect between the 1° non-working harmonics of the armature magnetic field and the other armature magnetic field harmonics of the magnetic field-modulated permanent magnet motor. As shown in FIG. 7, the 1* non-working harmonics of the armature magnetic field are independent of the other harmonics, and thus the 1* non-working harmonics of the armature magnetic field are relatively independent non-working harmonics of the armature magnetic field. step 5.1: Since the 1* relatively independent non-working harmonics of the armature magnetic field exist, the 1 relatively independent non-working harmonics of the armature magnetic field and the remaining armature magnetic field harmonics are optimized separately to reduce dimensions of the design parameters and the optimization objectives and increase the accuracy of the armature magnetic field harmonic optimization results. The 1* relatively independent non-working harmonics of the armature magnetic field are optimized first, and the design parameters highly sensitive to the 1* relatively independent non-working harmonics of the armature magnetic field are selected through the sensitivity analysis. As shown in FIG. 8, the design parameters 4» and wy are of high sensitivity, and a Kriging model of the design parameters in relation to the 1* relatively independent non- working harmonics of the armature magnetic field is built based on 4 and ws. As shown in FIG. 9, an optimal design point of the relatively independent non-working harmonics of the armature magnetic field is selected according to the built Kriging model. The optimization model of the relatively independent non-working harmonics of the armature magnetic field in the step 5.1 is expressed as follows: Objectives : Min[ 4 Hai(x,)] where x3 represents the design parameters A» and wp having great influences on the relatively independent non-working harmonics of the armature magnetic field after the sensitivity analysis, Ha represents the 1° relatively independent non-working harmonics of the armature magnetic field, 4 is a weighting coefficient corresponding to the relatively independent non-working harmonics of the armature magnetic field, and minimum values of the optimization model are optimization objectives. step 5.2: The working harmonics of the armature magnetic field and the remaining not relatively independent non-working harmonics of the armature magnetic field are optimized. A design parameter range limited by the amplitude of the synthesized working harmonics of the permanent magnetic field is taken as a constraint, and the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field are taken as the optimization objectives. A multi-objective genetic algorithm is used to optimize the working harmonics and the non-working harmonics of the armature magnetic field of the motor, an optimal Pareto frontier diagram of the armature harmonics (as shown in FIG. 10) is obtained, and a motor design scheme with optimal armature harmonics based on the high amplitude of the synthesized permanent magnet working harmonics is determined to realize the permanent magnet-armature magnetic field double-harmonic collaborative optimization design and improve the torque density and the power factor of the motor. As shown in FIG. 11, the torque density of the optimized magnetic field-modulated permanent magnet motor is increased from 26.2 Nm / L to 30.9 Nm / L and the power factor is increased from 0.49 to 0.7, which verifies the effectiveness of the proposed optimization design method. The optimization model of the working harmonics of the armature magnetic field and the simplified remaining not relatively independent non-working harmonics of the armature magnetic field in the step 5.2 is expressed as follows: Objectives : Max[H ,(x,)], Min[p,Has(x, +14, Hari(x,)] Constraint: f,(x,) >0 where Hop, represents P," working harmonics of the armature magnetic field of the motor and has maximum values set as optimization objectives, ensuring that the optimized motor has high torque; uoHao(xs) + pnHan(xs) represents simplified synthesized non-working harmonics of the armature magnetic field of the motor and has minimum values set as optimization objectives; x4 represents the remaining design parameters ws, Wp, Wm, Wa, and hn, after the design parameters x; are excluded from the total design parameters x1; Hao and Han represent ninth and eleventh non-working harmonics of the armature magnetic field, and uo and u11 are weighting coefficients corresponding to the ninth and the eleventh non-working harmonics of the armature magnetic field, respectively; Has represents the 31°* working harmonics of the armature magnetic field and us is a weighting coefficient corresponding to the 31* working harmonics of the armature magnetic field; and fi(x2) is a value range function of the design parameters limited by the synthesized working harmonics of the permanent magnetic field. In this specification, descriptions with reference to the terms "one embodiment”, "some embodiments", "exemplary embodiments", "examples", "specific examples", "some examples" and the like denote that the specific features, structures, materials, or characteristics illustrated by the embodiments or examples are incorporated in at least one embodiment or example of the present disclosure. In this specification, the schematic statements of the above terms do not necessarily mean the same embodiments or examples. Moreover, the illustrated specific features, structures, materials, or characteristics can be properly combined in any one or more embodiments or examples. Although the embodiments of the present disclosure have been shown and described, persons of ordinary skill in the art can understand that various changes, modifications, replacements, and variations can be made to these embodiments without departing from the principle and purpose of the present disclosure. The scope of the present disclosure is defined by the appended claims and their equivalents.

Claims

CLAIMS ‘What is claimed is: I. A permanent magnet-armature double-harmonic collaborative optimization design method for a magnetic field-modulated permanent magnet motor, characterized by comprising the following steps: step 1: establishing an expression of permanent magnet flux linkages in relation to permanent magnetic field harmonics and establishing an expression of armature flux linkages in relation to armature magnetic field harmonics according to a harmonic characteristic formula of a permanent magnetic field and a harmonic characteristic formula of an armature magnetic field, respectively; establishing an expression of a power factor in relation to the permanent magnet and armature flux linkages according to a flux linkage vector diagram of the magnetic field-modulated permanent magnet motor and obtaining an expression of the power factor in relation to the permanent magnet and armature magnetic field harmonics; analyzing, through the expression, influences of the flux linkages corresponding to the permanent magnet and armature magnetic field harmonics on torque and the power factor according to changes in size of a torque working area along with the permanent magnet and armature flux linkages in the vector diagram, and establishing permanent magnet- armature double-harmonic collaborative optimization design thoughts to improve a torque density and the power factor of the motor; dividing the permanent magnetic field harmonics into working harmonics of the permanent magnetic field and non-working harmonics of the permanent magnetic field based on whether the permanent magnetic field harmonics contribute to the torque, wherein the permanent magnetic field harmonics contributing to the torque are working harmonics of the permanent magnetic field, and the permanent magnetic field harmonics not contributing to the torque are non-working harmonics of the permanent magnetic field, weighting the working harmonics of the permanent magnetic field in each order to obtain synthesized working harmonics of the permanent magnetic field, wherein the permanent magnet flux linkages corresponding to the synthesized working harmonics of the permanent magnetic field are directly proportional to the torque and the power factor, so that when an amplitude of the synthesized working harmonics of the permanent magnetic field is enlarged, the power factor is increased and the torque density remains high; dividing the armature magnetic field harmonics into working harmonics of the armature magnetic field and non-working harmonics of the armature magnetic field based on whether the armature magnetic field harmonics contribute to the torque, wherein the armature magnetic field harmonics contributing to the torque are working harmonics of the armature magnetic field, and the armature magnetic field harmonics not contributing to the torque are non-working harmonics of the armature magnetic field; the flux linkages corresponding to the non-working harmonics of the armature magnetic field are inversely proportional to the power factor according to the expression of the flux linkages and the power factor; meanwhile, according to the flux linkage vector diagram, a decrease in the non-working harmonics of the armature magnetic field does not influence the size of the corresponding torque working area, so that the non-working harmonics of the armature magnetic field are decreased to increase the power factor without reducing the torque density; determining, according to analysis of the vector diagram and the power factor expression of the motor, that when the synthesized working harmonics of the permanent magnetic field at a high level are ensured, a minimum value of the non-working harmonics of the armature magnetic field and a maximum value of the working harmonics of the armature magnetic field are optimized to realize the permanent magnet-armature magnetic field double-harmonic collaborative optimization design and improve the torque density and the power factor of the motor; step 2: limiting the amplitude of the synthesized working harmonics of the permanent magnetic field, wherein a minimum value of the amplitude of the synthesized working harmonics of the permanent magnetic field is taken as a constraint, and design parameters having great influences on the working harmonics of the permanent magnetic field are selected through sensitivity analysis; an optimization model of the synthesized working harmonics of the permanent magnetic field is built based on the design parameters highly sensitive to the working harmonics of the permanent magnetic field; a relationship between the amplitude of the synthesized working harmonics of the permanent magnetic field and the design parameters highly sensitive to the working harmonics of the permanent magnetic field is expressed by using a Kriging model; a corresponding variation range of the design parameters highly sensitive to the working harmonics of the permanent magnetic field is obtained based on the built Kriging model according to the set minimum amplitude of the synthesized working harmonics of the permanent magnetic field in the optimization model; step 3: simplifying armature magnetic field harmonic optimization objectives, wherein since the armature magnetic field harmonics in a large number of orders are to be optimized, the armature magnetic field harmonic optimization objectives need to be simplified to reduce the number of the optimization objectives; sensitivity of the armature magnetic field harmonics to motor performance is analyzed and the highly sensitive armature magnetic field harmonics are selected as the optimization objectives; distribution of the armature magnetic field harmonics is calculated according to an experimental design method; the non-working harmonics of the armature magnetic field in a changing trend different from the working harmonics of the armature magnetic field are selected as the harmonics to be optimized according to an experimental point distribution diagram of the armature magnetic field harmonics, and the simplified armature magnetic field harmonic optimization objectives are obtained by weighting; step 4: judging independence of the non-working harmonics of the armature magnetic field, wherein an interaction effect between the armature magnetic field harmonics is calculated to analyze and judge whether relatively independent non-working harmonics exist in the armature magnetic field harmonics; if the relatively independent non-working harmonics of the armature magnetic field exist, steps 5.1 and 5.2 are performed; and if the relatively independent non-working harmonics of the armature magnetic field do not exist, step 5.3 is performed; step 5.1: if the relatively independent non-working harmonics of the armature magnetic field exist, optimizing the relatively independent non-working harmonics of the armature magnetic field and the remaining armature magnetic field harmonics separately to reduce dimensions of the design parameters and the optimization objectives and increase accuracy of armature magnetic field harmonic optimization results, wherein the relatively independent non-working harmonics of the armature magnetic field are optimized first, the design parameters highly sensitive to the relatively independent non-working harmonics of the armature magnetic field are selected through sensitivity analysis, a Kriging model of the design parameters in relation to the relatively independent non- working harmonics of the armature magnetic field is built, and an optimal design point of the relatively independent non-working harmonics of the armature magnetic field is selected according to the built Kriging model; step 5.2: optimizing the working harmonics of the armature magnetic field and the remaining not relatively independent non-working harmonics of the armature magnetic field, wherein a design parameter range limited by the amplitude of the synthesized working harmonics of the permanent magnetic field is taken as a constraint, the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field are taken as the optimization objectives, a multi-objective genetic algorithm is used to optimize the working harmonics and the non-working harmonics of the armature magnetic field of the motor, and a motor design scheme with optimal armature harmonics based on the high amplitude of the synthesized permanent magnet working harmonics is determined to realize the permanent magnet-armature magnetic field double- harmonic collaborative optimization design and improve the torque density and the power factor of the motor; step 5.3: optimizing the working harmonics and the non-working harmonics of the armature magnetic field, wherein the parameter range limited by the amplitude of the synthesized working harmonics of the permanent magnetic field is taken as a constraint, the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field are taken as the optimization objectives, the multi-objective genetic algorithm is used to optimize the working harmonics and the non-working harmonics of the armature magnetic field of the motor, and a motor design scheme with optimal armature harmonics based on the high amplitude of the synthesized permanent magnet working harmonics is determined to realize the permanent magnet- armature magnetic field double-harmonic collaborative optimization design and improve the torque density and the power factor of the motor.

2. The permanent magnet-armature double-harmonic collaborative optimization design method for the magnetic field-modulated permanent magnet motor according to claim 1, characterized in that: the harmonic characteristic formula of the permanent magnetic field B»(6,f) and the harmonic characteristic formula of the armature magnetic field B4(6,7) in the step 1 are as follows: B (60,t)=F, (6,1) x A (0) > C,A,cos(mPO-mPQNO+= > > C,A,cos[(mP. £kN,)6 —-mPQ,1] a np THRE Ng ee a m=13,5 m=135.k=1,23 B (6,1)=F,(60,t)x A (6) = DA cos(i@+PQ,1)+Y DA cos(j6—PQ,1) 1s YY. DA, cos[(i+kN,)0+PQ1]+ 2 i k=123. * 1 © © 2X >. DA, cos[(j£kN,)0—PQ,] J k=1,23. wherein Cy is a Fourier coefficient of a permanent magnet magnetomotive force, D; and D; are Fourier coefficients of an armature magnetomotive force, m is an order of the permanent magnet magnetomotive force, k is an order of permeance, 7 and j are orders of the armature magnetomotive force, P, is a number of permanent magnet pole pairs, Q- is a mechanical speed of the motor, 7 is time, Ao and Ay are Fourier coefficients of air-gap permeance, and N; is a number of armature slots; according to the expressions, the permanent magnetic field harmonics are in the orders of mP, and mPr + kN;, the armature magnetic field harmonics are in the orders of 7, j, i + kN, and j = kN;, and F4(6,r) represents the armature magnetomotive force; the permanent magnet magnetomotive force F(0,t) and the air-gap permeance A(8) are expressed as follows: FE, 6,)= Y C,cos(mP6—-mPQ,1) m=135, AB)=A+ > A, coskN 6 k=523, 3. The permanent magnet-armature double-harmonic collaborative optimization design method for the magnetic field-modulated permanent magnet motor according to claim 1, characterized in that: the expression of the permanent magnet flux linkages in relation to the permanent magnetic field harmonics in the step 1 is as follows: AIN, CL 2.0 =rln[ B, 2r len. amP. CA, EL sin =r cosmP.Q,t > m=1,3,5. mP, N, “+ Cally lhe ABER) pa ot I ¥:r m=1335.k=1,23. 2 mPxtkN, N, wherein 7; is a radius of an air gap, / ris an axial length, and nc is a number of winding turns; a fundamental amplitude of the permanent magnet flux linkages is expressed as follows: 2rl.n, vn =CA, Ze Gn TE P N, + CA, 21], 10 i oe sin TE EMV) > k=1,2,3. 2 PtkN, N, wherein C; is a fundamental Fourier coefficient of the permanent magnet magnetomotive force.

4. The permanent magnet-armature double-harmonic collaborative optimization design method for the magnetic field-modulated permanent magnet motor according to claim 1, characterized in that: the expression of the armature flux linkages in relation to the armature magnetic field harmonics in the step 1 is as follows: IN, oh B,(6,0)dt 0=rln| 2r ln i 2r ln j = 3 DA, Ee in TD cos PO + S DA, Zee sin cosPOt sm — N, a N, wil ED DA, 2r ln, Lomi Zo DA, rn, mj Zit Tee en Zk Zee ein 2 Led Coin —cos BQ, t+y, 9. —L EES Csin—Lcos BQ Sets. 2 ixkN, ON, TT S545. 2 jzRN, ON, wherein a fundamental amplitude of the armature flux linkages is expressed as follows: & 2rln - 2rl,n i y, = S DA, Zee sin ZL Sp A, See gin ZL N = N, Tl Miz allel, | TT) +> y SE _E9 fgn—1y 2 ixkN, N, 035. 2 JjxkN, N, DA ily; sin ¥ 3 DA, 2rd, nL 2 ithN, N, S435. 2 JjfkN, NWN, 5. The permanent magnet-armature double-harmonic collaborative optimization design method for the magnetic field-modulated permanent magnet motor according to claim 1, characterized in that: the expression of the power factor in relation to the permanent magnet and armature flux linkages in the step 1 is as follows: 2) 2 PF mers =o [1120 tur 0) U DQ. wherein ¢. represents magnetic flux leakage, p represents the permanent magnet flux linkages, ¢wa represents the flux linkages corresponding to the working harmonics of the armature magnetic field, pn. represents the flux linkages corresponding to the non-working harmonics of the armature magnetic field, U and w; are respectively phase voltage and frequency, and Ey is a back electromotive force of the permanent magnet.

6. The permanent magnet-armature double-harmonic collaborative optimization design method for the magnetic field-modulated permanent magnet motor according to claim 1, characterized in that: a sensitivity calculation formula in the step 2 is expressed as follows: NY xY(x)-D xD Y(x) i SOs (LA NY V(x) — (LY (3) wherein ¥(x) represents the amplitudes of the permanent magnet and armature magnetic field harmonics under different design parameters, N is a number of samples, and x represents the design parameters of the motor; the sensitivity analysis in the step 2 is specifically implemented as follows: sampling second- order factor design points, axis points, and zero-level center points in accordance with a second-order regression rotation criterion by using a central composite design sampling method to provide data support for sensitivity calculation; calculating, through the sensitivity formula, the sensitivity of different design parameters to the working harmonics of the permanent magnetic field, and selecting the highly sensitive design parameters to limit the amplitude of the synthesized working harmonics of the permanent magnetic field; after the sensitivity analysis, the built optimization model of the synthesized working harmonics of the permanent magnetic field is expressed as follows: He, = a,H,,(x,) h Constraint: H_,(x,)> g, wherein Hn is the amplitude of the synthesized working harmonics of the permanent magnetic field of the motor, x2 represents the design parameters highly sensitive to the permanent magnetic field harmonics of the motor, Hy is an amplitude of A" working harmonics of the permanent magnetic field, an is a weighting coefficient corresponding to the working harmonics of the permanent magnetic field, and gi is a minimum constraint value of the synthesized working harmonics of the permanent magnetic field.

7. The permanent magnet-armature double-harmonic collaborative optimization design method for the magnetic field-modulated permanent magnet motor according to claim 1, characterized in that: the simplified armature magnetic field harmonic optimization objectives in the step 3 are obtained through the sensitivity analysis and the experimental point distribution of the armature magnetic field harmonics, wherein the central composite design sampling method is used for sampling to provide data support for sensitivity calculation; the sensitivity of different armature magnetic field harmonics to the power factor is calculated through the sensitivity formula and the highly sensitive magnetic field harmonics are selected as the armature harmonic optimization objectives; the experimental point distribution diagram of the armature magnetic field harmonics is drawn according to the experimental points in the composite design sampling method; according to changing trends of different armature magnetic field harmonics in the diagram, the non-working harmonics of the armature magnetic field in a changing trend different from the working harmonics of the armature magnetic field are selected as the harmonics to be optimized, and the non-working harmonics of the armature magnetic field in a same changing trend as the working harmonics of the armature magnetic field are not taken as the harmonics to be optimized; and the harmonics to be optimized are linearly weighted to be optimization objectives, so that the number of the armature magnetic field harmonic optimization objectives is reduced for simplification of the armature magnetic field harmonic optimization objectives.

8. The permanent magnet-armature double-harmonic collaborative optimization design method for the magnetic field-modulated permanent magnet motor according to claim 1, characterized in that: the optimization model of the relatively independent non-working harmonics of the armature magnetic field in the step 5.1 is expressed as follows: Objectives : Min[» 4 Ha(x;)] wherein x3 represents the design parameters having great influences on the relatively independent non-working harmonics of the armature magnetic field after the sensitivity analysis, Ha represents / * relatively independent non-working harmonics of the armature magnetic field, 4: is a weighting coefficient corresponding to the relatively independent non-working harmonics of the armature magnetic field, and minimum values of the optimization model are optimization objectives; the optimization model of the working harmonics of the armature magnetic field and the simplified remaining not relatively independent non-working harmonics of the armature magnetic field in the step 5.2 is expressed as follows: Objectives : Max[H ,, (x,)], Min[Y_ x, Has(x,)] Constraint: f,(x,) >0 wherein Hp, represents P,™ working harmonics of the armature magnetic field of the motor and has maximum values set as optimization objectives, ensuring that the optimized motor has high torque; > MH, Has(x,) represents simplified synthesized non-working harmonics of the armature magnetic field of the motor and has minimum values set as optimization objectives; x4 represents the remaining design parameters after the design parameters x; are excluded from total design parameters x1, Has represents s™ non-working harmonics of the armature magnetic field, and us represents a weighting coefficient corresponding to the s™ non-working harmonics of the armature magnetic field; and fi(x2) is a value range function of the design parameters limited by the synthesized working harmonics of the permanent magnetic field.

9. The permanent magnet-armature double-harmonic collaborative optimization design method for the magnetic field-modulated permanent magnet motor according to claim 1, characterized in that: the optimization model of the working harmonics of the armature magnetic field and the simplified non-working harmonics of the armature magnetic field in the step 5.3 is expressed as follows: Objectives : Max[H,, (x;)], Min[Y pu, Hes(x,)] Constraint: f(x,)>0 wherein Hp: represents the P»* working harmonics of the armature magnetic field of the motor and has maximum values set as optimization objectives, ensuring that the optimized motor has high torque; y MH, Has(x;) represents the simplified synthesized non-working harmonics of the armature magnetic field of the motor and has minimum values set as optimization objectives; x1 represents the total design parameters of the motor, x, represents the design parameters highly sensitive to the permanent magnetic field harmonics of the motor, Hes represents the s* non-working harmonics of the armature magnetic field, and us represents the weighting coefficient corresponding to the s* non- working harmonics of the armature magnetic field; and fi(x2) is the value range function of the design parameters limited by the synthesized working harmonics of the permanent magnetic field.

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