WO2018072296A1

WO2018072296A1 - Teaching and learning algorithm-based calculation method for permanent magnet synchronous motor design

Info

Publication number: WO2018072296A1
Application number: PCT/CN2016/110686
Authority: WO
Inventors: 钱伟; 陈虎威
Original assignee: 钱伟
Priority date: 2016-10-19
Filing date: 2016-12-19
Publication date: 2018-04-26
Also published as: CN106528948A

Abstract

A teaching and learning algorithm-based calculation method for permanent magnet synchronous motor design, comprising: ten structural parameters of a permanent magnet synchronous motor will be taken as optimization variables. The method specifically comprises the following steps: 1. a mathematical model; 2. a novel improved teaching and learning algorithm; (1) a teaching stage; (2) a learning stage; 3. constraints; The present invention applies a novel improved teaching and learning algorithm and combines with Ansys finite element software to achieve optimal structural parameters for designing a permanent magnet synchronous motor so as to minimize the value of a target function and simplify an actual model, thereby achieving the purposes of reducing loss and cost of the motor and reducing volume, and meeting performance requirements of the motor. The motor efficiency may reach 97.5%, power factor is increased to 0.95, and the cost of each motor is reduced by 270 yuan. The calculation method is simple and easy to apply in an actual system, thereby further improving the speed and accuracy of the algorithm.

Description

A calculation method for design of permanent magnet synchronous motor based on teaching and learning algorithm

Technical field

The invention relates to a calculation method for a permanent magnet synchronous motor design based on a teaching and learning algorithm.

technical background

In China, electric motors are both a major consumer of electricity and the most energy-saving potential. According to the latest IEC standards, the United States has enforced the IE3 standard since 2010, and the average motor efficiency is close to 92%; European countries have enforced the IE2 standard since 2011, and the average motor efficiency is about 90%. China has formulated motor energy efficiency standards as early as 2002, and has been revised several times. In 2011, some of the minimum energy efficiency standards were enforced. However, the current energy efficiency of electric motors in China is still generally in the IE1 standard, with an average efficiency of about 87%. There is a gap that cannot be ignored in the country. Therefore, the design and promotion of high-efficiency and energy-saving motors are imperative in China.

The permanent magnet motor generates a magnetic field by the permanent magnet, so that the excitation winding and the excitation power supply are not needed, the structure is simple, the loss is relatively small compared with the electric excitation motor, and the utility model has the advantages of high efficiency and high power density.

The design theory of traditional electric excitation motor is relatively perfect, which provides a reference and reference for the design and analysis of permanent magnet motor. However, the permanent magnet motor has many new features that are different from the electric excitation motor; the structure is special and various in form, the magnetic field is difficult to adjust after fabrication, the electromagnetic load is high, the starting performance is not ideal, the permanent magnet has the risk of loss of magnetism, the loss of the motor is large, and the volume is large. Big, costly, and so on. Obviously, traditional design theory, empirical parameters and analytical calculation methods have been difficult to meet the requirements of developing high-performance permanent magnet motors. It is also necessary to comprehensively apply motor theory, electromagnetic field theory, magnetic materials, numerical calculation, simulation technology, testing technology and software engineering. Multi-disciplinary theory and modern design methods, innovative design in the key technology of permanent magnet motor design. To achieve the goal of energy saving and emission reduction, the designed motor must not only meet the performance requirements, but also meet the lower production costs.

Summary of the invention

In view of the main problems in the prior art permanent magnet synchronous motor, the need to solve the optimization goal is the loss, volume and cost of the motor.

A calculation method for the design of a permanent magnet synchronous motor based on a teaching and learning algorithm, which can overcome the above problems existing in the prior art. The object of the present invention is achieved in that a calculation method of a permanent magnet synchronous motor design based on a teaching and learning algorithm, including 10 structural parameters of a permanent magnet synchronous motor, is taken as an optimization variable, specifically: a magnetic pole pair (p ), polar arc coefficient (β), magnet thickness (l _m ), stator or rotor core thickness (l _y ), stator slot height (l _w ), air gap thickness (l _g ), rotor radius (r _r ), current Density (J _cu ), motor form factor (λ), winding cross-sectional area (A _c ); in the optimization process of slotless permanent magnet brushless DC motor, relevant specifications are also given, including material-determined windings Fill factor k _f , remanence B _{r of} permanent magnet, flux density at stator core or rotor core BH curve node

The electromagnetic torque T _em necessary for the normal operation of the motor and the rotational speed ω _r when the motor is stably operated are characterized in that the method specifically includes the following steps:

A mathematical model

Do some simplifying and neglect processing on the mathematical model of the motor, construct and determine the objective function of the optimization; in the permanent magnet synchronous motor designed by the invention, the loss of the motor, the material cost and the volume of the stator or rotor will be the most important factors to consider. The three indicators will be minimized at the same time; therefore, the objective function is written:

Min f(x)=w _c C(x)+w _v V _t (x)+w _p p _l (x) (2.1)

x=[p β l _m l _y l _w l _g r _r λ A _c ] ^T (2.2)

In equation (2.1), w _p , w _c and w _v are weight coefficients, P _l is the sum of electrical, magnetic and mechanical power losses, C is the cost of the material required for the motor, and V _t is the volume of the stator or rotor, where x Indicates the results of the required solution, including the nine structural parameters of the permanent magnet synchronous motor: pole pair (p), pole arc coefficient (β), magnet thickness (l _m ), stator or rotor core thickness (l _y ), stator Groove height (l _w ), air gap thickness (l _g ), rotor radius (r _r ), motor form factor (λ), winding cross-sectional area (A _c ). (2.2) where T represents the transpose of the result matrix. Expressed by the formula as follows:

V _t =πl _s (r _r +l _g +l _w +l _y ) ² (2.4)

p _l =p _cu +p _h +p _e +p _b (2.5)

Where ρ _m , ρ _w and ρ _y are the mass densities of the magnet, the coil and the stator or rotor core, respectively, c _m1 , c _m2 , and c _y represent the cost of the corresponding material unit, respectively, and c ₁ and c ₂ represent constants. , l _s represents the iron core length of the motor; the cost of the motor magnetic steel sheet is divided into the cost of the magnetic steel sheet material and the processing cost of sticking the magnetic steel sheet on the rotor;

The three-phase current is passed through the stator coil, and the copper consumption and skin effect are expressed as:

At the same time, the hysteresis loss and eddy current loss generated on the stator and rotor are expressed as:

The mechanical loss generated by the motor is mainly the friction loss of the motor bearing, and the relationship between the inner diameter of the stator and the rotor is expressed as:

p _b =μ _b ν(r _r +l _g ) ² l _s (2.9)

ν=60f/p (2.10)

In the above (2.1)-(2.10), m represents the phase number of the motor through voltage, ρ represents the resistivity of the stator winding, η and μ _cu represent the empirical constant, f represents the voltage frequency, V _sy represents the volume of the stator core, V _ry Represents rotor core volume, k _f , k _c , k _et , k' _h , k' _e and μ _b represent constants;

A new and improved teaching and learning algorithm

(1) Teaching stage

In the teacher stage of the new improved teaching and learning optimization algorithm, a mutation strategy similar to the difference algorithm is used to update the entire population; in this strategy, in addition to the teacher exerts influence, another gradient decreases direction ▽ (X _p -X _q ) has also been introduced; the purpose is to further improve the global search ability of the algorithm, avoiding the premature convergence under the guidance of only the teacher;

Here Global optimal is the global optimal solution, and the teacher is the current local optimal solution. By learning from a better solution, the solution gradually approaches the global optimal solution.

The following expression clearly states that the teacher and an arbitrary gradient direction indicate the direction for each individual update. The specific mathematical expressions are as follows:

Where X _i is randomly selected from the population to be updated, X _p and X _q are two individuals randomly selected from the population, and i≠p≠q, X _{i, new} are new solutions generated after updating. . Rand1 and rand2 are random numbers that satisfy the (0, 1) uniform distribution. It can be seen from the formula (2.11) that the update direction of the new individual is highly oriented. In addition to the teacher's guidance, there is another guidance for the direction of the descending gradient; all the search steps in the descending direction are at (0, 1). between;

(2) Academic stage

In this student phase, each individual will randomly learn from other individuals, with a smaller learning factor F. Allow small-step fine-tuning, but convergence is slower; a larger learning factor F can speed up convergence, but at the same time reduce local search ability; considering the above factors, in the early part of the iterative process, the learning factor F takes a large value to speed up The optimization speed of the algorithm; in the later stage of the iteration, since the optimization result is close to the optimal solution, the learning factor F is smaller and thus strengthens the local search ability; a new type of learning factor value distribution is adopted, which will further strengthen the local search ability. In order to prevent the occurrence of premature convergence, the search performance of the algorithm is further enhanced;

F=normrnd(1-FES/Max_FES,0.5*rand) (2.12)

Where X _s and X _t are 2 individuals randomly selected from the population, and i≠s≠t. To ensure a newly generated solution, F takes a positive value. At the same time, F conforms to the normal distribution, which is expressed as F ~ N (μ, σ ^ 2). The probability law of random variables following normal distribution is that the probability of taking the value adjacent to μ is large, and the probability of taking the value farther away from μ is smaller; the smaller the σ is, the more concentrated the distribution is near μ, the larger σ is, the more dispersed the distribution is. . μ=1-FES/Max_FES, σ=0.5*rand. We can see that as the iteration continues, μ changes from 1 to 0, and F falls from a large probability around 1 to a large probability of falling near zero.

The learning factor distribution at this stage is shown in Figure 2 (where the sequence number 1 indicates the random number F segment when the random number is 1.0; the sequence number 2 indicates the F segment when the random number is 0.75; the sequence number 3 indicates that the random number is 0.5. When the F division situation; the serial number 4 indicates the F division when the random number is 0.25). 1.0, 0.75, 0.5, 0.25 are values of different σ.

The probability that the random number generated by N(μ, σ^2) falls between [μ-σ, μ+σ] is 68.27%. Fig. 3(a), μ=1, when σ=0.25, the probability that the random number of the function value generated by the normal distribution falls between (0.75, 1.25) is 68.27%; Fig. 2(b), μ=0 When σ=0.25, the probability that the random number of the function value generated by the normal distribution falls between (-0.25, 0.25) is 68.27%;

Constraint conditions

First, considering the requirements for the motor output torque, the calculation formula used is as follows:

In formula (2.14), k _Nm represents the waveform coefficient, k _z represents the fundamental winding coefficient, A represents the electrical load, B _δ represents the magnetic load, and D _a1 represents the inner diameter of the stator, and D _a1 = r _r + l _{g is} defined.

Second, for the motor efficiency requirements, the following formula is used:

Finally, the constraints on the power factor of the motor are constrained by the following formula:

In the above formula (2.16), U _N and I _N represent the rated voltage and rated phase current of the motor, respectively.

Benefits of the Invention: The present invention applies a new and improved teaching and learning algorithm, and combines Ansys finite element software to realize the optimal structural parameters of the permanent magnet synchronous motor, so that the value of the objective function is minimized, and some important assumptions and settings are Introduced into the motor design to simplify the actual model, to reduce motor loss and cost, reduce the volume, meet the motor performance requirements, motor efficiency of 97.5%, power factor increased to 0.95, each cost reduced by 270 yuan. Moreover, the invention is improved on the basis of the classical teaching and learning algorithm, and the creative learning process is added, the calculation method is simple, and the application of the actual system is facilitated, and the speed and the accurate algorithm can be further improved.

DRAWINGS

1 is a schematic structural view of a permanent magnet synchronous motor;

Figure 2 teacher stage update strategy map;

Figure 3 learning factor distribution map (a);

Figure 4 learning factor distribution map (b);

Figure 5 is a trough profile of a permanent magnet synchronous motor;

Figure 6 Table 1 optimization variables and their range of three-phase permanent magnet synchronous motor;

Figure 7 shows the constant values set in the three-phase permanent magnet synchronous motor;

Figure 8 Table 3 comparison of the conventional method and the optimization scheme of the present invention;

1. stator yoke; 2. stator slot height; 3. magnetic steel sheet; 5-1. stator coil; 5-2. stator core punching; 5-3. magnetic steel sheet

detailed description

Example 1

In order to illustrate the superiority and effectiveness of the method, the method is applied to the design of a 355 kW-4-6 kV, 2000 rpm high speed three-phase permanent magnet synchronous motor. According to the requirements of motor performance, size, and working environment factors, in addition to the data requirements of Tables 1 and 2, the following constraints should be met:

Second, for the motor efficiency requirements, the following formula is used:

Therefore, using the method proposed by the present invention, combined with the formula (2.1)-(2.2) and the constraint conditions (2.14)-(2.16), the optimization variables and ranges of the three-phase permanent magnet synchronous motor of Table 1, the two-phase permanent The constant value set in the magnetic synchronous motor, the stator slot of the motor adopts a straight slot, and the obtained result is as follows.

x=[4 0.75 12 100 80 18 160 1.2 2.45] ^T

At this time, the calculated motor core length is 310mm, the motor efficiency is 0.975, the electromagnetic torque is 172.9N.m, and the power factor is 0.95, which fully meets the motor performance coefficient requirement. The slot profile of the motor is shown in Figure 5:

Table 1 Optimized variables and their range of three-phase permanent magnet synchronous motor

Table 2 Constant values set in three-phase permanent magnet synchronous motor

Table 3 Comparison of traditional methods and optimization schemes of the present invention

It is worth noting that in Table 3, we use N35UH magnetic steel sheets in the two methods used, and the traditional method mainly refers to the method designed according to the actual installation dimensions of the motor combined with experience. As can be seen from the above Table 3, by adopting the design method of the present invention, not only the production cost of the motor can be reduced, but also the working performance of the motor can be improved.

Claims

A calculation method for permanent magnet synchronous motor design based on teaching and learning algorithm, including 10 structural parameters of permanent magnet synchronous motor will be used as optimization variables, specifically: magnetic pole logarithm (p), polar arc coefficient (β), Magnet thickness (l m ), stator or rotor core thickness (l y ), stator slot height (l w ), air gap thickness (l g ), rotor radius (r r ), current density (J cu ), motor form factor (λ), winding cross-sectional area (A c ); in the optimization process of the slotless permanent magnet brushless DC motor, relevant specifications are also given, including the material-determined winding fill factor k f , the remaining of the permanent magnet Magnetic B r , magnetic flux density at the stator core or rotor core BH curve node
The electromagnetic torque T em necessary for the normal operation of the motor and the rotational speed ω r when the motor is stably operated are characterized in that the method specifically includes the following steps:

A mathematical model

Do some simplifying and neglect processing on the mathematical model of the motor, construct and determine the objective function of the optimization; in the permanent magnet synchronous motor designed by the invention, the loss of the motor, the material cost and the volume of the stator or rotor will be the most important factors to consider. The three indicators will be minimized at the same time; therefore, the objective function is written:

Min f(x)=w c C(x)+w v V t (x)+w p p l (x) (2.1)

x=[p β l m l y l w l g r r λ A c ] T (2.2)

In equation (2.1), w p , w c and w v are weight coefficients, P l is the sum of electrical, magnetic and mechanical power losses, C is the cost of the material required for the motor, and V t is the volume of the stator or rotor, where x Indicates the results of the required solution, including the nine structural parameters of the permanent magnet synchronous motor: pole pair (p), pole arc coefficient (β), magnet thickness (l m ), stator or rotor core thickness (l y ), stator Groove height (l w ), air gap thickness (l g ), rotor radius (r r ), motor form factor (λ), winding cross-sectional area (A c ). (2.2) where T represents the transpose of the result matrix. Expressed by the formula as follows:

V t =πl s (r r +l g +l w +l y ) 2 (2.4)

p l =p cu +p h +p e +p b (2.5)

Where ρ m , ρ w and ρ y are the mass densities of the magnet, the coil and the stator or rotor core, respectively, c m1 , c m2 , and c y represent the cost of the corresponding material unit, respectively, and c 1 and c 2 represent constants. , l s represents the iron core length of the motor; the cost of the motor magnetic steel sheet is divided into the cost of the magnetic steel sheet material and the processing cost of sticking the magnetic steel sheet on the rotor;

The three-phase current is passed through the stator coil, and the copper consumption and skin effect are expressed as:

At the same time, the hysteresis loss and eddy current loss generated on the stator and rotor are expressed as:

The mechanical loss generated by the motor is mainly the friction loss of the motor bearing, and the relationship between the inner diameter of the stator and the rotor is expressed as:

p b =μ b ν(r r +l g ) 2 l s (2.9)

ν=60f/p (2.10)

In the above (2.1)-(2.10), m represents the phase number of the motor through voltage, ρ represents the resistivity of the stator winding, η and μ cu represent the empirical constant, f represents the voltage frequency, V sy represents the volume of the stator core, V ry Represents the rotor core volume, k f , k c , k et , k' h , k′ e and μ b represent constants;

A new and improved teaching and learning algorithm

(1) Teaching stage

In the teacher stage of the new improved teaching and learning optimization algorithm, a mutation strategy similar to the difference algorithm is used to update the entire population; in this strategy, in addition to the teacher exerts influence, another gradient decreases direction ▽ (X p -X q ) has also been introduced; the purpose is to further improve the global search ability of the algorithm, avoiding the premature convergence under the guidance of only the teacher;

The following expression clearly states that the teacher and an arbitrary gradient direction indicate the direction for each individual update. The specific mathematical expressions are as follows:

Where X i is randomly selected from the population to be updated, X p and X q are two individuals randomly selected from the population, and i≠p≠q, X i, new are new solutions generated after updating. . Rand1 and rand2 are random numbers that satisfy the (0, 1) uniform distribution. It can be seen from the formula (2.11) that the update direction of the new individual is highly oriented. In addition to the teacher's guidance, there is another guidance for the direction of the descending gradient; all the search steps in the descending direction are at (0, 1). between;

(2) Academic stage

In this student stage, each individual will randomly learn from other individuals. The smaller learning factor F allows fine tuning of small steps, but the convergence is slower; the larger learning factor F can accelerate convergence, but at the same time it reduces local search ability. Considering the above factors, in the early stage of the iterative process, the learning factor F takes a large value to speed up the optimization of the algorithm; in the later stage of the iteration, since the optimization result is close to the optimal solution, the learning factor F takes a small value to strengthen the local Search ability; a new type of learning factor value distribution is adopted, which will further strengthen the local search ability to prevent the occurrence of premature convergence, and further improve the search performance of the algorithm;

F=normrnd(1-FES/Max_FES,0.5*rand) (2.12)

Where X s and X t are two individuals randomly selected from the population, and i ≠ s ≠ t, F take a positive value; at the same time F conforms to the normal distribution, which is expressed as F ~ N (μ, σ ^ 2); The probability law of random variables following normal distribution is that the probability of taking the value adjacent to μ is large, and the probability of taking the value farther away from μ is smaller; the smaller the σ is, the more concentrated the distribution is near μ, the larger σ is, the more dispersed the distribution is. . μ=1-FES/Max_FES, σ=0.5*rand; as the iteration continues, μ changes from 1 to 0, and F becomes a large probability to fall around 0 from a large probability;

The learning factor distribution at this stage is the case of the random number F when the random number is 1.0; the F part when the random number is 0.75; the F part when the random number is 0.5; when the random number is 0.25, F Divisional situation; 1.0, 0.75, 0.5, 0.25 are the values of different σ, which are visually represented by graphs;

The probability that the random number generated by N(μ, σ^2) falls between [μ-σ, μ+σ] is 68.27%; when μ=1, σ=0.25, it represents the value of the function generated by the normal distribution. The probability that the random number falls between (0.75, 1.25) is 68.27%; when μ=0, when σ=0.25, the probability that the random number of the function value generated by the normal distribution falls between (-0.25, 0.25) Is 68.27%;

Constraint conditions

First, considering the requirements for the motor output torque, the calculation formula used is as follows:

In formula (2.14), k Nm represents the waveform coefficient, k z represents the fundamental winding coefficient, A represents the electrical load, B δ represents the magnetic load, and D a1 represents the inner diameter of the stator, defining D a1 = r r + l g ;

Second, for the motor efficiency requirements, the following formula is used:

Finally, the constraints on the power factor of the motor are constrained by the following formula:

In the above formula (2.16), U N and I N respectively represent the rated voltage and rated phase current of the motor;

Using the method proposed by the present invention, combined with the formulas (2.1)-(2.2) and the constraints (2.14)-(2.16), the optimization variables and ranges of the three-phase permanent magnet synchronous motor of Table 1, the two-phase permanent magnet synchronization of Table 2 The constant value set in the motor, the stator slot of the motor adopts a straight slot, and the calculated motor core length, motor efficiency, electromagnetic torque, and power factor fully meet the motor performance coefficient requirements.