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The purpose of this paper is to execute the efficiency analysis of the selected metaheuristic algorithms (MAs) based on the investigation of analytical functions and investigation optimization processes for permanent magnet motor.

A comparative performance analysis was conducted for selected MAs. Optimization calculations were performed for as follows: genetic algorithm (GA), particle swarm optimization algorithm (PSO), bat algorithm, cuckoo search algorithm (CS) and only best individual algorithm (OBI). All of the optimization algorithms were developed as computer scripts. Next, all optimization procedures were applied to search the optimal of the line-start permanent magnet synchronous by the use of the multi-objective objective function.

The research results show, that the best statistical efficiency (mean objective function and standard deviation [SD]) is obtained for PSO and CS algorithms. While the best results for several runs are obtained for PSO and GA. The type of the optimization algorithm should be selected taking into account the duration of the single optimization process. In the case of time-consuming processes, algorithms with low SD should be used.

The new proposed simple nondeterministic algorithm can be also applied for simple optimization calculations. On the basis of the presented simulation results, it is possible to determine the quality of the compared MAs.

The purpose of this paper is to elaborate the effective method of adaptation of the external penalty function to the genetic algorithm.

In the case of solving the optimization tasks with constraints using the external penalty function, the penalty term has a larger value than the primary objective function. The sigmoidal transformation is introduced to solve this problem. A new method of determining the value of the penalty coefficient in subsequent iterations associated with the changing penalty has been proposed. The proposed approach has been applied to the optimization of an electromagnetic linear actuator, and the mathematical model of the devices contains equations of the magnetic field, by taking into account the nonlinearity of ferromagnetic material.

The proposed new approach of the penalty function method consists in the reduction of the external penalty function in successive penalty iterations instead of its increase as it is in the classical method. In addition, the method of normalization of constraints during the formulation of optimization problem has a significant impact on the obtained results of optimization calculations.

The proposed approach can be applied to solve constrained optimization tasks in designing of electromagnetic devices.

The purpose of this paper is to develop an algorithm and software for determining the size of a line-start permanent magnet synchronous motor (LSPMSMs) based on its optimization.

The software consists of an optimization procedure that cooperates with a FEM model to provide the desired behavior of the motor under consideration. The proposed improved version of the genetic algorithm has modifications enabling efficient optimization of LSPMSMs. The objective function consists of three important functional parameters describing the designed machine. The 2-D field-circuit mathematical model of the dynamics operation of the LSPMSMs consists of transient electromagnetic field equations, equations describing electric windings and mechanical motion equations. The model has been developed in the ANSYS Maxwell environment.

In this proposed approach, the set of design variables contains the variables describing the stator and rotor structure. The improved procedure of the optimization algorithm makes it possible to find an optimal motor structure with correct synchronization properties. The proposed modifications make the optimization procedure faster and more

This proposed approach can be successfully applied to solve the design problems of LSPMSMs.

The purpose of this paper is to compare parameters and properties of optimal structures of a line-start permanent magnet synchronous motor (LSPMSM) for the cage winding of a different rotor bar shape.

The mathematical model of the considered motor includes the equation of the electromagnetic field, the electric circuit equations and equation of mechanical equilibrium. The numerical implementation is based on finite element method (FEM) and step-by-step algorithm. To improve the particle swarm optimization (PSO) algorithm convergence, the velocity equation in the classical PSO method is supplemented by an additional term. This term represents the location of the center of mass of the swarm. The modified particle swarm algorithm (PSO-MC) has been used in the optimization calculations.

The LSPMSM with drop type bars has better performance and synchronization parameters than motors with circular bars. It is also proved that the used modification of the classical PSO procedure ensures faster convergence for solving the problem of optimization LSPMSM. This modification is particularly useful when the field model of phenomena is used.

The authors noticed that to obtain the maximum power factor and efficiency of the LSPMSM, the designer should take into account dimensions and the placement of the magnets in the designing process. In the authors’ opinion, the equivalent circuit models can be used only at the preliminary stage of the designing of line-start permanent magnet motors.

The purpose of this paper is to elaborate an algorithm and the computer code for the optimization of the permanent magnet synchronous motor (PMSM) including the shaft torque, the cogging torque, the total harmonic distortion factor of the back EMF and magnet volume into compromise objective function.

The mathematical model of the device includes the magnetic field equations with the nonlinearity of the magnetic core taken into account. The numerical implementation is based on the finite element method (FEM) and time stepping procedure. The genetic algorithm has been applied for the optimization. The comprehensive computer code containing the FEM model and optimization procedures have been elaborated.

Very important problem at formulating the optimization task is the choice of the functional parameters which constitute the objective and constraint functions. In the paper it has been shown that uncritical constructing the objective function could lead to irrational variants of the designed object. Authors pointed out (Knypiński et al., 2013) that connecting the shaft torque and the cogging torque simultaneously into the one compromise objective function generates ineffective operation of the optimization algorithm and often also leads to the non-optimal result.

Authors proved that in case of multi-criterion objective function composed of terms which have very different impact on this function value (i.e. very diverse sensitivity of the objective function for these terms is observed) than the optimization process can be significantly distorted. Therefore, decomposition of the optimization process into two stages has been proposed. Some of the parameters (e.g. cogging torque) have been excluded from the first stage of the process. The two stage algorithm has been successfully implemented and tested on the example of PMSM machine.

The purpose of this paper is to elaborate the algorithm and computer code for the structure optimization of the outer rotor permanent magnet brushless DC motor and to execute optimization of selected motor structure using the non‐deterministic procedure.

The mathematical model of the device includes the electromagnetic field equations with the nonlinearity of the magnetic core taken into account. The numerical implementation is based on the finite element method and stepping procedure. The genetic algorithm has been applied for the optimization. The computer code has been elaborated.

The elaborated computer software has been applied for the optimization and design of BLDC motors. The elaborated algorithm has been tested and a good convergence has been attained.

The presented approach and computer software can be successfully applied to the design and optimization of different structure of BLDC motors.

The purpose of this paper is to elaborate the methodology and software for the optimization of rotor structure of the line-start permanent magnet synchronous motor (LSPMSM). To prove usefulness of presented approach the case study problem has been solved.

The modified particle swarm optimization (PSO) algorithm has been employed for the optimization of LSPMSM. The optimization solver has been elaborated in Delphi environment. The software consists of two modules: an optimization solver and a numerical model of LSPMSM. The model of the considered machine has been developed in the ANSYS Maxwell environment. In the optimization procedure the objective function has been based on maximizing efficiency and power factor.

Obtained results show that modified PSO algorithm can be successfully applied for the optimization of the rotor structure of LSPMSM. This software can be used as a design tool to improve the performance of LSPMSM. The results of studied case problem illustrate that it is possible to optimize rotor of LSPMSM to achieve good self-starting properties with simultaneous minimization of usage of permanent magnet material.

Both, the simpler lumped parameters model and more advanced field model of the motor were tested. Presented comparison to the results of the finite element analysis (FEA) shows that for considered in the paper the case study problem the accuracy of circuit model is acceptable.

Presented approach and developed software can be used as an effective design tool to improve the performance of LSPMSM.

The paper offers appropriate approach for optimizing the permanent magnet synchronous motors having ability to start by direct connection to the grid.

The purpose of this paper is to elaborate an algorithm and the software for the rotor structure optimization of the permanent magnet synchronous motor (PMSM) with a magnet composed of two materials made with the use of different technologies: sintered Neodymium magnets and powder dielectromagnets. To execute of optimization of selected motor structure using the non-deterministic procedure.

The mathematical model of the devices includes: the equation of the electromagnetic field, the electric circuit equations and equation of mechanical motion. The numerical implementation is based on finite element method and step-by-step algorithm. The genetic algorithm has been applied in the optimization procedures. The computer code has been developed.

The elaborated computer software has been applied for the optimization and design of PMSMs. The elaborated algorithm has been tested and a good convergence has been attained. The parameters of two optimal structures of PMSM motors have been compared.

The presented approach and computer software can be successfully applied to the design and optimization of different structure of PMSM with different type of rotors.

The purpose of this paper is to elaborate a mathematical model of dynamic operation of the permanent magnet brushless DC (BLDC) motor with outer rotor and investigate the influence of magnets width on the dynamic parameters.

The mathematical model of the devices includes: the equation of the electromagnetic field, the electric circuit equations and equation of mechanical motion. In elaborated algorithm, all these equations are coupled – therefore they are solved simultaneously. The numerical implementation is based on finite element method and step‐by‐step algorithm. The non‐linear‐coupled field‐circuit equations have been solved by using the Newton‐Raphson algorithm. The computer code for dynamics simulation of the machine has been developed.

The elaborated algorithm and the computer code have been applied for the 2D simulation of BLDC motor dynamics. The algorithm has a good convergence and its usefulness was proved. Various results of the analysis are presented and discussed.

The presented approach and computer code can be successfully applied to the design and optimization of different structure of the BLDC motors.