CN116861720B - Multi-objective layered optimization method for field modulation motor based on power factor expansion - Google Patents
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Abstract
The invention discloses a field modulation motor multi-objective hierarchical optimization method based on power factor expansion, and belongs to the technical field of motor body design and analysis. According to the invention, parameters such as inductance, counter potential and the like are expanded in detail according to the traditional power factor expression, so that the power factor expansion based on the magnetic field modulation ratio of the motor and various structural parameters is obtained, and the influence of the structural parameters on the power factor of the motor can be intuitively seen from the expression for the permanent magnet surface-mounted concentrated winding field modulation motor. By combining the power factor expansion, taking the power factor, the torque pulsation and the average torque as optimization targets, a multi-target optimization algorithm is introduced to decouple and layer a plurality of optimization variables and optimization targets, the optimization process is simplified, the optimization time is saved, and the power factor of the motor is improved.
Description
Technical Field
The invention relates to the technical field of motor body design and analysis, in particular to a field modulation motor multi-objective layering optimization method based on power factor expansion.
Background
With the intensive research of the field modulation theory, the theory is gradually applied to the topology of the motor, and is different from the traditional permanent magnet synchronous motor in that the pole pair numbers of the permanent magnet and the pole pair numbers of the armature winding of the field modulation motor are different, so that the speed of a rotating magnetic field generated by the field modulation motor and the armature winding is different, and the field modulation motor can realize low-speed direct drive. However, as the research goes deep, the scholars find that because the field modulated motor is coupled by using the harmonics in the magnetic field, this causes the power factor of this type of motor to be generally not high, which means that a larger capacity converter is provided when the motor is used, which increases the cost. How to increase the power factor of a field modulated motor is a hotspot of current research on field modulated motors.
Disclosure of Invention
The invention aims to solve the technical problem of providing a multi-objective layered optimization method of a field modulation motor based on power factor expansion, so as to solve the problem of lower power factor caused by magnetic field modulation ratio and structural parameters of the existing permanent magnet surface-mounted field modulation motor.
In order to solve the technical problems, the invention provides the following technical scheme:
a field modulation motor multi-objective hierarchical optimization method based on power factor expansion comprises the following steps:
step 1: carrying out formula expansion on magnetic potential flux guide of the field modulation motor in a normal running state to obtain each phase and a flux linkage expression generated between the phases, so as to obtain an expression of self inductance and mutual inductance of the motor, and simultaneously considering the influence of slot leakage inductance and tooth tip leakage inductance;
step 2: converting a stationary phase coordinate system into a dq axis coordinate system through coordinate transformation, carrying out formula derivation on q axis inductance of the field modulation motor, and substituting the q axis inductance expression of the field modulation motor into the motor self inductance and mutual inductance expression obtained in the step 1 to obtain a q axis inductance expression of the field modulation motor; in addition, according to the formation mechanism of the counter potential of the motor, deriving a counter potential expression of the motor;
step 3: substituting the q-axis inductance expression and the counter potential expression into a traditional permanent magnet motor power factor expression, and deforming and expanding the formula to obtain a magnetic field modulation ratio related to a field modulation motor power factor and a quantitative expression of structural parameters, thereby judging which parameters have decisive influence on the field modulation motor power factor;
step 4: selecting proper optimization variables according to the power factor expansion derived in the step 3, and simultaneously taking the power factor, the torque pulsation and the average torque as optimization targets to expand multi-target optimization, and screening out two different optimization layers;
step 5: and respectively adopting a modeling method of finite element modeling and response surface modeling for two different optimization layering, and simultaneously adopting an optimization algorithm to complete multi-objective optimization and improve the power factor of the field modulation motor.
The invention has the following beneficial effects:
according to the multi-objective layered optimization method for the field modulation motor based on the power factor expansion, parameters such as inductance, counter potential and the like are expanded in detail according to the traditional power factor expression, so that the power factor expansion based on the magnetic field modulation ratio of the motor and various structural parameters is obtained, and the influence of the structural parameters on the power factor of the motor can be intuitively seen from the formula for the permanent magnet surface-mounted concentrated winding field modulation motor. By combining the power factor expansion, taking the power factor, the torque pulsation and the average torque as optimization targets, a multi-target optimization algorithm is introduced to decouple and layer a plurality of optimization variables and optimization targets, the optimization process is simplified, the optimization time is saved, and the power factor of the motor is improved.
Drawings
FIG. 1 is a flow diagram of a power factor expansion-based field modulation motor multi-objective hierarchical optimization method of the present invention;
FIG. 2 is a structural model of a subject centralized permanent magnet surface mount field modulated motor under investigation in the present invention;
FIG. 3 is a two-dimensional planar model of a motor under study in the present invention and its local dimensioning;
FIG. 4 is a schematic diagram of magnetomotive force generated by a single armature winding coil of interest in the present invention;
FIG. 5 is a graph of the internal magnetic field vectors studied in the present invention;
FIG. 6 is a schematic diagram of optimization variables for multi-objective optimization in accordance with the present invention;
FIG. 7 is a graph of sensitivity factors for various optimization variables for multi-objective optimization in accordance with the present invention;
FIG. 8 is a flow chart of the multi-objective optimization studied in the present invention;
FIG. 9 is a three-dimensional schematic of a response surface model constructed by multi-objective optimization in accordance with the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages to be solved more apparent, the following detailed description will be given with reference to the accompanying drawings and specific embodiments.
In order to research the essential reason of low power factor of the field modulation motor, the power factor expression of the field modulation motor is expanded, which is different from the prior patent application 202110411560.6 (a high power factor design method of the field modulation permanent magnet fault-tolerant motor) and 202210909057.8 (a magnetic field modulation permanent magnet motor optimization method considering magnetic leakage and air gap magnetic field harmonic waves), the power factor expansion in the method provided by the application can more intuitively reflect the characteristics of structural parameters influencing the power factor of the field modulation motor, and simultaneously embody the direct relation between the power factor of the field modulation motor and the magnetic field modulation ratio, and more directly reveal the characteristics of the power factor of the field modulation motor.
The invention provides a field modulation motor multi-objective hierarchical optimization method based on power factor expansion, which is shown in fig. 1 and comprises the following steps:
step 10: carrying out formula expansion on magnetic potential flux guide of the field modulation motor in a normal running state to obtain each phase and a flux linkage expression generated between the phases, so as to obtain an expression of self inductance and mutual inductance of the motor, and simultaneously considering the influence of slot leakage inductance and tooth tip leakage inductance;
for the permanent magnet motor, when the motor operates, main magnetic flux for useful work is also leakage magnetic flux including slot leakage magnetic flux, tooth top leakage magnetic flux and end leakage magnetic flux, in this step, in order to accurately calculate the inductance of the field modulation motor, the flux potential flux guide of the field modulation motor in the normal operation state is subjected to formula expansion, and the magnetomotive force generated by a single coil is shown in fig. 4, so that each phase and flux linkage expression generated between phases are obtained, and the expressions of self inductance and mutual inductance of the motor are obtained, and meanwhile, the influence of slot leakage inductance and tooth top leakage inductance is considered.
As an alternative embodiment, in the step 10, the obtained expressions of self inductance and mutual inductance of the motor, that is, the expressions of self inductance and mutual inductance of each phase of the armature winding, are respectively:
wherein t is the number of loops of the motor unit, lambda δ Is the flux guide on the air gap flux path, f 1 (x) Is magnetomotive force inside the coil, f 2 (x) To magnetomotive force outside the coil, ψ 1 For flux linkage passing inside the coil, ψ 2 Is the flux linkage passing through the outside of the coil, I is the current magnitude, g e The equivalent air gap length of the thickness of the permanent magnet is considered, N is the number of turns of the armature winding, mu 0 Is vacuum permeability, D is the diameter at the circumference of the air gap, l ef The effective length of the stator core is y is the armature winding pitch, and m is the armature winding phase number.
In the invention, the field modulation motor is preferably a permanent magnet surface-mounted concentrated winding field modulation motor, and the structure is shown in fig. 2, wherein 1 is a rotor, 2 is a stator, 3 is modulation teeth, 4 is magnetic steel (S pole), 5 is magnetic steel (N pole), and 6 is an armature winding. FIG. 3 is a two-dimensional model of the motor, where h pm The thickness of the permanent magnet, g is the length of an air gap, g e B is equivalent air gap length 1 Is the width of the groove bottom, b 2 For the width of the notch, h 1 Is the groove depth.
Step 20: converting a stationary phase coordinate system into a dq axis coordinate system through coordinate transformation, carrying out formula derivation on q axis inductance of the field modulation motor, and substituting the q axis inductance expression of the field modulation motor into the motor self inductance and mutual inductance expression obtained in the step 10 to obtain a q axis inductance expression of the field modulation motor; in addition, according to the formation mechanism of the counter potential of the motor, deriving a counter potential expression of the motor;
in the step, dq conversion is introduced, a three-phase motor coordinate conversion method is used for reference, a stationary phase coordinate system (six-phase full symmetry) is converted into a dq axis coordinate system through coordinate conversion, formula derivation is carried out on q axis inductance of the field modulation motor, and meanwhile, the q axis inductance expression of the field modulation motor is obtained by substituting the expression of self inductance and mutual inductance of the motor obtained in the step 10; in addition, the counter potential expression of the motor is derived from the formation mechanism of the counter potential of the motor.
As an alternative embodiment, in the step 20, the q-axis inductance expression and the counter potential expression are respectively:
wherein lambda is σ Is the slot ratio flux leakage guide of a single-layer winding, Z is the number of slots of a motor stator, and k is the number of slots of the motor stator w For armature winding coefficient, τ is stator tooth pole arc coefficient, p r Is the pole pair number, omega of the permanent magnet r Is the mechanical angular velocity of the rotor in rad/s, B av The magnetic flux is close to the air gap close to the tooth side of the stator in the air gap of the motor.
Step 30: substituting the q-axis inductance expression and the counter potential expression into a traditional permanent magnet motor power factor expression, and deforming and expanding the formula to obtain a magnetic field modulation ratio related to a field modulation motor power factor and a quantitative expression of structural parameters, thereby judging which parameters have decisive influence on the field modulation motor power factor;
in this step, the q-axis inductance expression and the counter potential expression obtained above are substituted into the traditional permanent magnet motor power factor expression, and the formulas are properly deformed and expanded, and a motor parameter vector diagram is shown in fig. 5, so that a quantitative expression of a magnetic field modulation ratio and a structural parameter related to the power factor of the field modulation motor is obtained, and from the quantitative expression, it can be intuitively judged which parameters have a decisive influence on the power factor of the surface-mounted field modulation motor.
As an alternative embodiment, the power factor expansion derived in the step 30 is:
wherein G is a magnetic field modulation ratio related to the number of pole slots in the motor, and g=p r /p s ω=2pi f, where p s The pole pair number of the armature winding is shown, ω is the angular velocity, and f is the motor operating frequency.
From the above expression, it can be seen that the number of turns N of the armature winding, the magnetic field modulation ratio G, and the air gap flux density B near the stator tooth side in the air gap av Diameter D at the air gap circumference, equivalent air gap length g e And the armature winding pitch y, have an effect on the power factor of the field modulated motor.
Step 40: according to the power factor expansion derived in the step 30, selecting a proper optimization variable, and simultaneously taking the power factor, the torque pulsation and the average torque as optimization targets to expand multi-target optimization, and screening out two different optimization layers;
in this step, according to the power factor expansion derived in step 30, an appropriate optimization variable is selected, as shown in fig. 6, and a multi-objective optimization is performed by using the power factor, the torque ripple and the average torque as optimization objectives, so as to simplify the optimization process, reduce the optimization time, preferably analyze each optimization variable by using a sensitivity factor (see fig. 7), synchronously decouple the optimization variable and the optimization objective according to the sensitivity, and screen two different optimization hierarchies, namely: optimizing layering I: permanent magnet thickness h pm Air gap length g versus torque pulseDynamic T rp Is a function of (1); optimizing layering II: stator tooth width d st Stator yoke thickness d sy Air gap radius R ag Inductance L to q axis q Back emf E 0 And average torque T ave Is a function of (1); wherein the q-axis inductance L q Back emf E 0 Indirectly reflecting the magnitude of the power factor, it is known from the power factor expansion that a higher power factor can be achieved with a smaller q-axis inductance and a larger back emf.
In specific implementation, the method for screening out the optimized layering in the step 40 may be: for each (in particular five) structural parameters (permanent magnet thickness h pm Air gap length g, stator tooth width d st Stator yoke thickness d sy Radius of air gap R ag ) The sensitivity factor calculation of the corresponding optimization targets is carried out, and according to the sensitivity, researches find that the thickness of the permanent magnet and the length of the air gap only have more obvious influence on torque pulsation, but have other three optimization targets: the q-axis inductance, the counter potential and the average torque have smaller influence, and the same can obtain that the stator tooth width and the stator yoke thickness have smaller influence on torque pulsation and larger influence on other three optimization targets, so that based on the research, the optimization variables and the optimization targets are decoupled and layered, and multi-target optimization is separately carried out.
Step 50: and respectively adopting a modeling method of finite element modeling and response surface modeling for two different optimization layering, and simultaneously adopting an optimization algorithm to complete multi-objective optimization and improve the power factor of the field modulation motor.
In this step, modeling methods of finite element modeling and response surface modeling (see fig. 9) are respectively adopted for two different layers, and meanwhile, an optimization algorithm is adopted, which can be various algorithms in the field, and in this embodiment, an experimental design and an artificial bee colony optimization algorithm are preferably adopted respectively, so that multi-objective optimization (see fig. 8) is successfully completed, and the power factor of the field modulation motor is improved. Preferably, for the optimization layering I, the permanent magnet thickness and the air gap length are taken as optimization variables, and the torque pulsation is taken as an optimization target; for optimization layer II, the stator tooth width, the stator yoke thickness and the air gap radius are taken as optimization variables, and q-axis inductance, counter potential and average torque are taken as optimization targets.
The test shows that the motor power factor is increased from 0.91 to 0.97.
In summary, the invention has the following beneficial effects:
1. according to the characteristic of the internal magnetic field of the permanent magnet surface-mounted field modulation motor, the quadrature axis inductance and the back electromotive force expression are solved, the traditional power factor is successfully expanded, the detailed expansion of the power factor of the permanent magnet surface-mounted field modulation motor is obtained, and the influence factors of the power factor of the permanent magnet surface-mounted field modulation motor are intuitively disclosed.
2. According to the invention, by means of the derived power factor expression, structural parameters with larger influence on the power factor are searched, the maximum power factor, the maximum average torque and the minimum torque pulsation are taken as optimization targets, meanwhile, the influence degree of each parameter on different targets is considered, and synchronous decoupling is carried out on the optimization variables and the optimization targets, so that the optimization process is simplified, the optimization time is saved, and meanwhile, a better optimization structure is obtained.
3. The invention starts from the expansion of the power factor, introduces a multi-objective optimization algorithm, successfully improves the power factor of the permanent magnet surface-mounted field modulation motor, solves the problem of low power factor of the field modulation motor, and provides a certain research thought for continuously researching the power factor of the field modulation motor in the next step.
While the foregoing is directed to the preferred embodiments of the present invention, it will be appreciated by those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the present invention.
Claims (5)
1. The field modulation motor multi-objective hierarchical optimization method based on power factor expansion is characterized by comprising the following steps of:
step 1: carrying out formula expansion on magnetic potential flux guide of the field modulation motor in a normal running state to obtain each phase and a flux linkage expression generated between the phases, so as to obtain an expression of self inductance and mutual inductance of the motor, and simultaneously considering the influence of slot leakage inductance and tooth tip leakage inductance;
step 2: converting a stationary phase coordinate system into a dq axis coordinate system through coordinate transformation, carrying out formula derivation on q axis inductance of the field modulation motor, and substituting the q axis inductance expression of the field modulation motor into the motor self inductance and mutual inductance expression obtained in the step 1 to obtain a q axis inductance expression of the field modulation motor; in addition, according to the formation mechanism of the counter potential of the motor, deriving a counter potential expression of the motor;
step 3: substituting the q-axis inductance expression and the counter potential expression into a traditional permanent magnet motor power factor expression, and deforming and expanding the formula to obtain a magnetic field modulation ratio related to a field modulation motor power factor and a quantitative expression of structural parameters, thereby judging which parameters have decisive influence on the field modulation motor power factor;
step 4: according to the power factor expansion derived in the step 3, selecting an optimization variable, and simultaneously taking the power factor, the torque pulsation and the average torque as optimization targets to expand multi-target optimization, and screening out two different optimization layers;
step 5: respectively adopting a modeling method of finite element modeling and response surface modeling for two different optimization layering, and simultaneously adopting an optimization algorithm to complete multi-objective optimization and improve the power factor of the field modulation motor;
in the step 1, the obtained expressions of self inductance and mutual inductance of the motor, namely, the expressions of self inductance and mutual inductance of each phase of the armature winding are respectively:
wherein t is a motor unitNumber of primary loops lambda δ Is the flux guide on the air gap flux path, f 1 (x) Is magnetomotive force inside the coil, f 2 (x) To magnetomotive force outside the coil, ψ 1 For flux linkage passing inside the coil, ψ 2 Is the flux linkage passing through the outside of the coil, I is the current magnitude, g e The equivalent air gap length of the thickness of the permanent magnet is considered, N is the number of turns of the armature winding, mu 0 Is vacuum permeability, D is the diameter at the circumference of the air gap, l ef The effective length of the stator core is y is the pitch of the armature winding, and m is the phase number of the armature winding;
in the step 2, the q-axis inductance expression and the back electromotive force expression are respectively:
wherein lambda is σ Is the slot ratio flux leakage guide of a single-layer winding, Z is the number of slots of a motor stator, and k is the number of slots of the motor stator w For armature winding coefficient, τ is stator tooth pole arc coefficient, p r Is the pole pair number, omega of the permanent magnet r Is the mechanical angular velocity of the rotor in rad/s, B av The motor is characterized in that the motor is close to the air gap flux density of the tooth side of the stator in the air gap;
the power factor expansion derived in the step 3 is as follows:
wherein G is a magnetic field modulation ratio related to the number of pole slots in the motor, and g=p r /p s ω=2pi f, where p s The pole pair number of the armature winding is shown, ω is the angular velocity, and f is the motor operating frequency.
2. The method according to claim 1, wherein in the step 4, each optimization variable is analyzed by using a sensitivity factor, the optimization variable and the optimization objective are decoupled according to the sensitivity, and two different optimization hierarchies are selected.
3. The method according to claim 2, wherein the step 5 is further: and respectively adopting a modeling method of finite element modeling and response surface modeling for two different optimization layering, and simultaneously respectively adopting an experimental design and an artificial bee colony optimization algorithm to complete multi-objective optimization and improve the power factor of the field modulation motor.
4. The method according to claim 2, wherein in step 5, the two different optimization hierarchies comprise an optimization hierarchy i and an optimization hierarchy ii, wherein for the optimization hierarchy i, permanent magnet thickness and air gap length are used as optimization variables, torque ripple is used as optimization target; for optimization layer II, the stator tooth width, the stator yoke thickness and the air gap radius are taken as optimization variables, and q-axis inductance, counter potential and average torque are taken as optimization targets.
5. The method of claim 1, wherein the field modulated motor is a permanent magnet surface mount concentrated winding field modulated motor.
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