The motor optimization design is a nonlinear optimization problem with inequality constraints that can be described as: where g is the constraint condition function, m is the number of constraints, n is the number of variables, and X is the vector of the independent variables.
Generally, the following are the main difficulties in the optimal design of the motor: 1) The accuracy of the mathematical model, ie, whether the error between the calculated value and the actual measured value of the electromagnetic calculation program is sufficiently small. In this regard, a lot of work has been done [1, 2], and the equivalent circuits and iterative algorithms used are very mature.
2) The selection of optimization algorithms, the text summarized almost all of the algorithms, many other literature work is to make these algorithms more practical. Among these algorithms, the most widely used is to solve the equivalent unconstrained problem such as the machine search method, the steepest descent method, the simplex method, and the Powell method that convert the constraint problem into a series of unconstrained problems. More advanced algorithms such as discrete direct search, simulated annealing, etc. are also well applied. However, all algorithms must solve two problems through improvement: one is the local convergence of the algorithm and the other is the dispersion of variables.
The optimization design method of asynchronous motor proposed in this paper, through the innovation of the motor design formula and the appropriate selection of optimization variables, not only solves the problem of variable dispersion, but also greatly improves the global convergence rate, and is suitable for almost all of the optimization numerical algorithms.
1 Motor Design Mathematical Model 1. 1 Design Strategy Currently there are two ways in the design process: traditional design method and direct design method.
The traditional design method follows three processes: selected dimensions - calculation parameters - check performance. This method can optimize the design scheme by understanding the effect of motor geometry and material consumption on the parameter performance, and obtain the optimal design result through continuous modification. The traditional design method requires designers to have a thorough understanding of the laws of motor design. In the design, they can grasp the main contradiction and find adjustment measures to solve the problem. The optimal design method established in this method is to use some of the most important variables that affect the motor parameters and performance.
The direct design method is actually the inverse calculation of the conventional design method. After the electromagnetic performance is determined, the relevant parameters only change within a very small range, and the specific geometric dimensions are finally determined. Its process can be described as: performance - parameter - size. This design method requires a lot of statistical data on the existing product as a basis for the experience, parameters and the size of the functional relationship is difficult to use mathematical models to express, so rarely create an optimal design method.
The design idea is to first determine the key performance parameters, get the geometric dimensions from the basic equations of the motor, and then follow the traditional design method to get the results of the parameters and performance calculations. The entire process can be described as: key performance determination - geometry - calculation parameters - check performance. This method can have a preliminary grasp of the design results of the motor at the beginning of the design. The size of each part of the motor can be obtained completely according to the process. The calculation shows that the initial set of parameter performance is very different from the final check result. These differences are also caused by the discreteness of certain design values ​​within the motor.
1. 2 main dimensions of the design formula The main equation in the motor design is: where: E is the stator potential, f is the rated frequency, W is the number of series stator per phase, D is the stator ID, L is the stator core length, n is the number of poles, B is the air gap magnetic density, P is the rated output power, m is the number of stator phases, U is the stator input phase voltage, I is the stator rated phase current, G is the motor efficiency, and cos H is the power factor.
In the traditional design formula, the line load can be expressed as the frequency associated with the synchronous speed n, which can be obtained to obtain the design formula of the main size of the motor: where c is approximately a constant, with which the effective rotor volume can be estimated, and then By using the ratio of the radial dimensions of the stator and rotor, the inner diameter of the stator and the length of the core can be separated from the effective volume. Obviously, the design formula of this major dimension does not take into account the design of the outer diameter of the stator, stator slots and stator rotors. The design of most of the size of the motor still needs to be done by experience.
Here is a new design formula, using formula (7) instead of formula (3): where: J is the stator current density, Q is the number of stator slots, and A is the stator slot copper area per slot.
The stator slot area can be obtained from Figure 1 where: b is the slot size.
From the stator magnetic load and the stator tooth width and yoke height h can be obtained: B is the stator tooth flux density, and B is the stator yoke flux density core lamination coefficient.
Then, the stator outer diameter is obtained from the geometry of the stator slot and equation (8).
Defining the copper-filling factor to be substituted into (7), and in conjunction with (1) (2) (4), a new design formula can be obtained: c is a constant, K = D is a function.
Equations (11)-(13) directly relate the stator and rotor volume to the electrical and magnetic loads of the motor, as long as the electrical and magnetic loads of the motor are determined, not only the main dimensions of the motor (including the stator inner, outer diameter and core length). ) can be determined, and the slot size of the stator and the amount of copper for the stator can also be determined. This makes the experience components in the motor design much less.
2 Selection of optimization variables The design formulae in the traditional design method, the optimization variables are generally taken as the key dimensions and parameters of the motor, such as the stator inner diameter Di1, the core length and the number of conductors per groove as the design variables and other effects on the performance Larger quantities such as stator slot width bs, stator slot Gao Mengkai, etc.: A new method for optimal design of asynchronous motors, rotor current density J, etc. can also be treated as variables. These variables basically determine the main parameters and performance of the motor, and are the optimal variables used by most motor optimization methods.
However, there are three disadvantages that can't be ignored in this method of selecting variables: a) The existence of discrete variables makes most of the optimization algorithms can not be used directly. As we all know, the length L of the core, the number of conductors Z per groove, etc. must be discrete due to processing. However, in most optimization algorithms, optimization must be performed in a continuous space. In this way, every general algorithm becomes uncommon in the motor optimization process. Some algorithms can solve discrete problems after being improved. Some algorithms are It is not considered suitable for motor optimization.
The relationship between optimization variables and motor performance cannot be visualized. Obviously, if you want to reduce the stator copper loss or reduce the iron loss, the above optimization variables do not give an intuitive and simple modification method. If the designer is not an experienced expert, then it is difficult for him to adjust the parameters to get the ideal design.
c) The optimization algorithm is difficult to achieve global convergence in the space of optimization variables.
As mentioned, the relationship between the optimization variables and the motor performance is not intuitive, which makes a lot of local extremum in the optimization space, and we want to cross these local extremum points to find the global maximum (small) point for the algorithm. The choice brings great difficulties. In fact, most of the optimization algorithms cannot overcome the problem of local convergence. To solve this problem, the traditional optimization method generally adopts a better selection of initial points so that the optimization process does not touch the local extreme points.
Selecting the electrical and magnetic loads of the motor and the copper filling rate of the stator and rotor slots as optimization variables can overcome all of the above shortcomings. Taking into account the factors of the motor series design, the optimization variables are selected as follows: where: K is the copper filling rate of the stator slot, and K is the copper filling rate of the rotor slot.
Obviously, all the optimization variables are continuous quantities. Using equations (11) to (13), other dimensions and parameters of the motor can be obtained directly. Since the optimization space is continuous, the existing algorithms no longer need to be modified in the motor optimization process, and the problem of discrete variables is naturally solved.
The size of the electrical load determines the rotor resistance and copper loss of the motor. The magnitude of the magnetic load determines the iron loss and power factor of the motor. The electromagnetic load also determines the efficiency of the motor. The copper filling rate determines the amount of material (copper) for the motor and The price, in turn, reflects approximately the slot full rate. This method of selecting parameters makes the motor design more intuitive and easier to grasp.
As the cross-effect between optimization variables and motor performance is greatly reduced, the local extreme points in the optimization space are also greatly reduced, which makes the possibility of the optimization algorithm in global convergence improved. Without changing the algorithm, only the optimization of the variable space can solve the problem of local convergence in the traditional optimization.
3 Optimization Mathematical Models and Numerical Algorithm 3.1 Objective Function This paper uses a single-objective optimization method. Aiming at all the concerns in the design of asynchronous motors, a dozen objective functions have been established for design and research. These include: material usage, effective material costs, efficiency, power factor, maximum torque, starting torque, starting current, and heat load. These objective functions are not necessarily fully used for design work, but their research will benefit the design.
3.2 Constraints The normal range of values ​​and performance indicators of all design parameters in the motor design constitute constraints.
The constraints used in this paper include three categories: 1) The range of constraints for the optimization variables, which is mainly to reduce the optimization calculation time and prevent the optimization of the calculation process from occurring anomalies. 2) The motor performance constraints are the same as the traditional optimization methods. Process and electromagnetic parameters are constrained, such as the range of the core length, the minimum slot size, the maximum slot full rate, and the highest yoke core density subject to saturation.
Because of the new design formula, the discrete values ​​in the motor size parameters are automatically processed, such as the selection rule, the number of conductors per slot, and the number of series turns per phase. Therefore, the new optimization design method does not contain discrete constraints.
3. 3 Numerical Algorithm In traditional motor optimization design, choosing an appropriate optimization algorithm is an important task. Because the optimization problem of the motor design is a nonlinear problem with inequality constraints, and the objective function and constraint conditions cannot generally be expressed as the explicit function of the design variables, so the motor design optimization algorithm chooses the direct method. In the direct method, it can not be applied to motor optimization design. The biggest difficulty is the dispersion of variables and the local convergence of the algorithm. In this paper, based on the new method, the algorithm (coordinate rotation method, Hooke method, method and simplex method for multidimensional optimization), complex algorithm, grid algorithm and boundary search algorithm are studied. The research shows that these new algorithms can be used directly in motor optimization design after adopting new design formulas and variable selection methods, and do not need to be adapted to discrete space optimization.
4 Examples This paper uses the optimization results of the algorithm and the complex algorithm as an example to verify the effectiveness of the new method.
The optimized objects are the Y optimization results in the Y series as shown in Table 1. T in the table is the rating of this quantity.
Tsinghua University (Science Edition) 280S4 motor optimization performance comparison table optimization object algorithm maximum torque starting torque starting current thermal load copper quantity optimization before the complex shape optimization before the complex objective function takes the efficiency G, as the frequency conversion The design of the speed-specific motor relaxes the constraints on starting performance. From the optimization results, we can see that using the new optimization method, the SUM T algorithm and the complex algorithm can give satisfactory results.
From the comparison of the two algorithms, the complex algorithm has a better optimization effect, but its disadvantage is that the initial point must be within the feasible region. Related Algorithm 5 Conclusion The motor optimization design strategy proposed in this paper is very different from the traditional design method in the design process and design formula. Based on the new design formula, a representative optimization variable is selected to solve the discrete problem in the traditional motor design. Optimization and local convergence problems.
The new optimization method gives the designer an opportunity to choose an optimization algorithm, on which basis the algorithm can be studied. The selection of optimization variables makes the adjustment of variables in the design process more intuitive and facilitates the establishment of expert systems and intelligent research on them.
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