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Global optimization of three-phase asynchronous motor based on random algorithm

classification number: tm343.3 document identification code: a

article number: (2000) the global optimization of energy-effective production

motors with a random method you Tong, Lu Jian Guo,

(Hebei University of technology, Tianjin 300130, China)

wei Shi Ze,

（Hebei University of Science and Technology, Shijiazhuang 050000, China）

ZHANG Guo-qiang

（Baoding Tianwei Corp.(Group), Baoding 071051, China）ABSTRACT：The optimization design of energy-efficient induction machines is a complex nonlinear problem with constraints. To solve the problem, this paper introduces a united random algorithm. At first, the problem is divided into two stages, the optimal rotor slots and the optimization of other dimensions. Before optimize the rotor slots with genetic algorithm (GA), the another stage has been solved with TABU algorithm to simplify the problem. The numerical results show that this method is acceptable for the practical design.

KEY WORDS：induction motors; global optimization; TABU search algorithm; Introduction in recent years, many countries have formulated new energy and environmental protection policies for various reasons. In response, major motor manufacturers around the world have launched their own series of "efficient" or "ultra efficient" cast aluminum rotor asynchronous motors. The pursuit of high efficiency of asynchronous motor is becoming a trend in the manufacturing industry, and efficiency based motor optimization is also widely concerned by the motor industry to catch the beneficial opportunistic technology that is revolutionizing biomaterial science and engineering

The optimization of cast aluminum rotor asynchronous motor is a complex nonlinear programming problem. Its complexity is mainly reflected in the following aspects: ① the problem involves many variables, and many variables are coupled with each other, and the state space is huge. Its state combination exceeds 1024 [1]. Therefore, it is difficult to traverse with a small step length. ② Whether efficiency, cost or some comprehensive index is used as the objective function, when optimizing variables such as rotor slot type, the problem shows strong non convexity and nonlinearity, local or even discontinuous. Therefore, when using deterministic methods for optimization, it is easy to fall into the local optimal solution and make its global optimization failwith the development of modern mathematics, many scholars have introduced stochastic approximation into optimization and proposed some new algorithm models, which provide a powerful algorithm tool for nonlinear programming. Genetic algorithm is especially suitable for finding the global optimal solution of complex functions because it does not depend on the gradient information of the problem. However, genetic algorithm also has the defects of large amount of computation and slow convergence. In order to solve this problem, firstly, the problem is decomposed, and the fast convergent tabu algorithm is used to pre optimize the convex like variables, so as to reduce the dimension of the problem, which greatly reduces the computational workload and meets the requirements of the actual design. 2 the basic algorithm used in this paper can be summarized as the following nonlinear programming problem

problem 1: Max f (x) GI (x) ≥ 0 (I = 1,2,..., m), where x ∈ xn is the optimization variable in the solution domain xn; F (x) is the objective function; GI (x) ≥ 0 is the constraint condition

in this paper, f (x) is set as the efficiency of the motor η； The constraints include: ① the locked rotor torque TST and the maximum torque TM of the motor are ≥ the standard values t 'st and t'm respectively. Huaibei City focuses on aluminum based new materials, high-precision aluminum plates, strips and foils, light-weight accessories for vehicles, and recycled aluminum; ② Locked rotor current ist ≤ standard value I ′ st; ③ Length of iron core L ≤ Lmax; ④ Electric density J, magnetic density B and thermal load AJ are not greater than the specified values jMax, Bmax and ajmax

considering the inheritance and manufacturability of the design scheme and in order to reduce the electromagnetic noise, additional loss and harmonic torque of the motor, the number of stator and rotor slots, winding pitch, air gap length g, stator and rotor diameter and rotor end ring size of the motor are generally determined in advance in the actual design. Then the optimization variable x is mainly composed of the following parameters: ① core length L; ② Winding turns N and wire diameter D; ③ Size of stator and rotor slot type (common slot type is shown in Figure 1). Figure 1. Among the above three groups of variables of the slots, the optimization of the rotor slot is usually considered to be the most difficult and complex. This is because: ① in the design of high-efficiency motors, TST and ist are usually the main constraints affecting the efficiency improvement, and only the youth who have made contributions to the people. The guarantee of TST and the limitation of ist are usually realized through the optimization of rotor slot type in actual design; ② In order to obtain the highest efficiency under the locked rotor constraint, various special-shaped slots are widely used in modern small and medium-sized asynchronous motors. Due to the influence of saturation and skin effect, the relationship between the locked rotor performance and the rotor slot parameters is extremely complex when using the field circuit combination method for calculation, and the functional properties are very poor. At the same time, the coupling between the slot sizes is also extremely close. In recent years, genetic algorithm has been widely used in solving this kind of optimization problems of discontinuous, irregular and non convex functions

genetic algorithm (GA) comes from the simulation experiment that some biologists use computers to simulate the process of biological evolution. In 1960, Professor Holland of Michigan University first applied it to solve practical optimization problems. This algorithm simulates the evolution process of survival of the fittest and genetic inheritance in nature, and uses variable coding technology to realize an algorithm through fitness information. The specific algorithm is as follows [2 ~ 4]:

(1) determine the algorithm parameters: total number of individuals n, crossover probability PC, mutation probability PM, generation gap G

(2) initialize the population, calculate the fitness fi of each individual, and determine the overlap between the two generations

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