Strategies for balancing exploration and exploitation in electromagnetic optimisationSong Xiao; Mihai Rotaru; Jan K. Sykulski
2013 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
doi: 10.1108/03321641311317004
Purpose – Electromagnetic design utilising finite element or similar numerical methods is computationally expensive, thus efficient algorithms reducing the number of objective function calls to locate the optimum are sought. The balance between exploration and exploitation may be achieved using a reinforcement learning approach, as demonstrated previously. However, in practical design problems, in addition to finding the global optimum efficiently, information about the robustness of the solution may also be important. In this paper, the aim is to discuss the suitability of different search algorithms and to present their fitness to solve the optimization problem in conjunction with providing enough information on the robustness of the solution. Design/methodology/approach – Two novel strategies enhanced by the surrogate model based weighted expected improvement approach are discussed. The algorithms are tested using a two‐variable test function. The emphasis of these strategies is on accurate approximation of the shape of the objective function to accomplish a robust design. Findings – The two novel strategies aim to pursue the optimal value of weights for exploration and exploitation throughout the iterative process for better prediction of the shape of the objective function. Originality/value – It is argued that the proposed strategies based on adaptively tuning weights perform better in predicting the shape of the objective function. Good accuracy of predicting the shape of the objective function is crucial for achieving a robust design.
Optimization of the permanent magnet brushless DC motor employing finite element methodŁukasz Knypiński; Lech Nowak
2013 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
doi: 10.1108/03321641311317013
Purpose – 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. Design/methodology/approach – 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. Findings – 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. Originality/value – The presented approach and computer software can be successfully applied to the design and optimization of different structure of BLDC motors.
A polynomial chaos meta‐model for non‐linear stochastic magnet variationsPeter Offermann; Kay Hameyer
2013 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
doi: 10.1108/03321641311317031
Purpose – Due to the production process, arc segment magnets with radial magnetization for surface‐mounted permanent‐magnet synchronous machines (PMSM) can exhibit a deviation from the intended ideal, radial directed magnetization. In such cases, the resulting air gap field may show spatial variations in angle and absolute value of the flux‐density. For this purpose, this paper aims to create and evaluate a stochastic magnet model. Design/methodology/approach – In this paper, a polynomial chaos meta‐model approach, extracted from a finite element model, is compared to a direct sampling approach. Both approaches are evaluated using Monte‐Carlo simulation for the calculation of the flux‐density above one sole magnet surface. Findings – The used approach allows representing the flux‐density's variations in terms of the magnet's stochastic input variations, which is not possible with pure Monte‐Carlo simulation. Furthermore, the resulting polynomial‐chaos meta‐model can be used to accelerate the calculation of error probabilities for a given limit state function by a factor of ten. Research limitations/implications – Due to epistemic uncertainty magnet variations are assumed to be purely Gaussian distributed. Originality/value – The comparison of both approaches verifies the assumption that the polynomial chaos meta‐model of the magnets will be applicable for a complete machine simulation.
Calculation of the flux distribution of three phase five limb power transformers considering nonlinear material propertiesBjörn Riemer; Enno Lange; Kay Hameyer
2013 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
doi: 10.1108/03321641311317059
Purpose – Depending on the load the flux‐density distribution inside power transformers core shows significant local variations due to stray fluxes which enter the transformer core. As saturation of the core has to be avoided the flux‐density distribution has to be determined early in the design stage of the transformer. This paper seeks to address these issues. Design/methodology/approach – To determine the load dependent flux‐density distribution the operating point of the transformer is calculated considering linear and non‐linear material properties. The operating point is determined using a linearised lumped parameter model of the transformer under various load conditions. Considering non‐linear material properties the inductance matrix depends on the operating point and will be extracted by means of the FEM whenever the magnetic energy within the transformer changes notably. Findings – This paper presents a numerical stable approach to calculate the operating point of a transformer by using the magnetic flux linkage as state variable for the coupled field problem. Research limitations/implications – The proposed approach uses a fixed time‐step to update the lumped parameters by means of the FEM. This results in long simulation times. In further research it is planned to implement an adaptive time‐step method based on the change of the magnetic energy. Originality/value – A numerical stable approach to calculate the operating point of a transformer by using the magnetic flux linkage as state variable for the coupled field problem is proposed. The methodology is applied to a 2D model of a three‐phase transformer. However, it also can be applied to 3D FE models. Based on the calculated operating point, the flux‐density distribution can be determined and several post‐processing methods can be executed (e.g. determination of core losses, …).
Modeling and experimental verification of a flexible rotor/AMB systemGoranka Štimac; Sanjin Braut; Neven Bulić; Roberto Žigulić
2013 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
doi: 10.1108/03321641311317068
Purpose – In this paper, the aim is to present a modeling strategy for a flexible rotor/active magnetic bearing (AMB) system with non‐collocation. Special attention is paid to the vibration reduction and the stable passage through the first critical speed. Design/methodology/approach – The finite element method based on Euller‐Bernoulli beam theory is applied in the formulation of the rotor model. Since rotor/AMB systems are complex mechatronic systems, reduced order approach is used in the control system design. This study applies the modal decomposition method and the modal truncation method, thus retaining the lower order bending modes. The obtained numerical results are compared with the measured open loop frequency responses and the existing differences are compensated in order to obtain accurate numerical model. Findings – Frequency response of the entire system model (flexible shaft, actuators, power amplifiers and sensors) with amplitudes expressed in rotor lateral displacements can be verified by the measured frequency responses. The deviations in the amplitude and phase diagrams are then successfully corrected using the appropriate model modifications. Practical implications – The results of this research find direct applications in flexible rotors supported by AMBs, e.g. high speed spindles, turbo molecular pumps, flywheel energy storage systems, etc. The presented procedure can be especially valuable in the design of model based controllers. Originality/value – An AMB system model is developed and presented in this paper, in conjunction with a systematic description of an efficient procedure for the elimination of the typical mismatches between the simulation and experiment. Firstly, rotor/AMB test rig is stabilized with an appropriately tuned PID controller and an open loop frequency response is obtained for such a system. This response is then compared to corresponding simulation results for which mismatches are identified and eliminated thus yielding an accurate model of the system.
Model of dynamic operation of stepper linear reluctance motor based on field approachJacek Mikołajewicz
2013 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
doi: 10.1108/03321641311317077
Purpose – The aim of this paper is to analyse the influence of various methods of controlling a stepper linear reluctance motor on the dynamic parameters of this motor. Design/methodology/approach – Construction, principle of working, and mathematical model of a four‐band stepper linear reluctance motor are shortly discussed. In order to elaborate an effective tool for motor performance analysis, a circuital approach was applied. To increase model accuracy, major parameters of the model (main self‐ and leakage inductances) were calculated on the basis of a 3D electromagnetic field distribution using Finite Element Method (FEM). The nonlinearity of the core was taken into account. Elaborated mathematical model was implemented in MatLab‐Simulink environment. Selected results of investigations are presented. Findings – The elaborated mathematical model and the review of control methods are very useful for analysis of dynamic operation of stepper linear reluctance motors. Originality/value – The paper provides a review of control methods of stepper linear reluctance motors.
Identification techniques of functions approximating magnetization characteristics of synchronous machinesAdam Warzecha; Witold Mazgaj
2013 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
doi: 10.1108/03321641311317086
Purpose – The aim of the paper is to present the approximation methods of the magnetizing characteristics of the salient pole synchronous machines with the fundamental MMF harmonics. Design/methodology/approach – The energy based approach is used to formulate a set of the functions approximating the magnetic flux linkages versus an equivalent magnetizing current in the circuit model of the synchronous machine. The estimation of the approximation functions parameters is based on the results of the field calculations. Findings – The identification of the approximation functions is effective and significantly simpler on the basis of the magnetic field co‐energy function, than on the basis of the magnetic flux linkages. Research limitations/implications – The magnetic field co‐energy function determined by FEM is sufficient for simplified calculations of the magnetic parameters occurring in the circuit models of the electrical machines with nonlinear core. Practical implications – The paper provides guidance for the circuit modelling of the multi‐pole generators and motors under conditions of magnetic saturation. Originality/value – A paper has succeeded in determining the internal magnetic characteristics of the synchronous machine with a salient pole rotor.
3D analysis of influence of stator winding asymmetry on axial fluxWojciech Pietrowski
2013 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
doi: 10.1108/03321641311317095
Purpose – The diagnostics of electrical machines is a very important task. The paper seeks to present a study and analysis of stator winding asymmetry in induction motors. The purpose of this paper is presentation of coupling two numerical techniques, a finite element analysis and an artificial neural network, in diagnostics of electrical machines. Design/methodology/approach – A finite element method (FEM) analysis and time‐stepping are applied for the study of IM with stator winding asymmetry. One of the asymmetry symptoms is an axial flux. In order to determine the level of winding asymmetry a generalized regression neural network has been considered. The result of FFT analysis of axial flux and electromagnetic torque was the input vector to artificial neural network. The output vector is the level of asymmetry. The algorithms are tested using a set data obtained from numerical simulation. The emphasis of this structure is on accurate approximation of the value of the stator winding asymmetry. Findings – The axial flux, as the symptom of stator winding asymmetry, can contribute to better detection of the asymmetry in stator winding. Originality/value – It is argued that the proposed method based on axial flux and electromagnetic torque is capable of performing detection of the asymmetry in stator winding. The generalized regression neural network can be used in health monitoring system as an inference module.